Alan Ruttenberg
Bill Duncan
Stefan Schulz
Melanie Courtot
BFO 2 Reference: BFO does not claim to be a complete coverage of all entities. It seeks only to provide coverage of those entities studied by empirical science together with those entities which affect or are involved in human activities such as data processing and planning – coverage that is sufficiently broad to provide assistance to those engaged in building domain ontologies for purposes of data annotation [17
Mark Ressler
Fabian Neuhaus
Thomas Bittner
Bjoern Peters
Mauricio Almeida
David Osumi-Sutherland
BFO 2 Reference: For both terms and relational expressions in BFO, we distinguish between primitive and defined. ‘Entity’ is an example of one such primitive term. Primitive terms in a highest-level ontology such as BFO are terms that are so basic to our understanding of reality that there is no way of defining them in a non-circular fashion. For these, therefore, we can provide only elucidations, supplemented by examples and by axioms.
Leonard Jacuzzo
Janna Hastings
Mathias Brochhausen
Randall Dipert
Larry Hunter
Robert Rovetto
Albert Goldfain
Chris Mungall
Barry Smith
Ludger Jansen
This is an early version of BFO version 2 and has not yet been extensively reviewed by the project team members. Please see the project site http://code.google.com/p/bfo/ , the bfo2 owl discussion group http://groups.google.com/group/bfo-owl-devel , the bfo2 discussion group http://groups.google.com/group/bfo-devel, the tracking google doc http://goo.gl/IlrEE, and the current version of the bfo2 reference http://purl.obolibrary.org/obo/bfo/dev/bfo2-reference.docx . This ontology is generated from a specification at http://bfo.googlecode.com/svn/trunk/src/ontology/owl-group/specification/ and with the code that generates the OWL version in http://bfo.googlecode.com/svn/trunk/src/tools/. A very early version of BFO version 2 in CLIF is at http://purl.obolibrary.org/obo/bfo/dev/bfo.clif
Werner Ceusters
Pierre Grenon
BFO 2 Reference: BFO’s treatment of continuants and occurrents – as also its treatment of regions, rests on a dichotomy between space and time, and on the view that there are two perspectives on reality – earlier called the ‘SNAP’ and ‘SPAN’ perspectives, both of which are essential to the non-reductionist representation of reality as we understand it from the best available science [30
Jonathan Bona
Ron Rudnicki
BFO OWL specification label
Really of interest to developers only
Relates an entity in the ontology to the name of the variable that is used to represent it in the code that generates the BFO OWL file from the lispy specification.
BFO CLIF specification label
Person:Alan Ruttenberg
Really of interest to developers only
Relates an entity in the ontology to the term that is used to represent it in the the CLIF specification of BFO2
has axiom label
definition
has associated axiom(nl)
editor note
has associated axiom(fol)
imported from
curator note
definition source
term editor
alternative term
elucidation
editor preferred term
example of usage
inheres in at all times
BFO 2 Reference: Inherence is a subrelation of s-depends_on which holds between a dependent continuant and an independent continuant that is not a spatial region. Since dependent continuants cannot migrate from one independent continuant bearer to another, it follows that if b s-depends_on independent continuant c at some time, then b s-depends_on c at all times at which a exists. Inherence is in this sense redundantly time-indexed.For example, consider the particular instance of openness inhering in my mouth at t as I prepare to take a bite out of a donut, followed by a closedness at t+1 when I bite the donut and start chewing. The openness instance is then shortlived, and to say that it s-depends_on my mouth at all times at which this openness exists, means: at all times during this short life. Every time you make a fist, you make a new (instance of the universal) fist. (Every time your hand has the fist-shaped quality, there is created a new instance of the universal fist-shaped quality.)
inheresInAt
inheres-in_at
(iff (inheresInAt a b t) (and (DependentContinuant a) (IndependentContinuant b) (not (SpatialRegion b)) (specificallyDependsOnAt a b t))) // axiom label in BFO2 CLIF: [051-002]
BFO2 Reference: independent continuant that is not a spatial region
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'inheres in at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'inheres in@en(x,y,t)'.
BFO2 Reference: specifically dependent continuant
b inheres_in c at t =Def. b is a dependent continuant & c is an independent continuant that is not a spatial region & b s-depends_on c at t. (axiom label in BFO2 Reference: [051-002])
b inheres_in c at t =Def. b is a dependent continuant & c is an independent continuant that is not a spatial region & b s-depends_on c at t. (axiom label in BFO2 Reference: [051-002])
(iff (inheresInAt a b t) (and (DependentContinuant a) (IndependentContinuant b) (not (SpatialRegion b)) (specificallyDependsOnAt a b t))) // axiom label in BFO2 CLIF: [051-002]
bearer of at some time
(iff (bearerOfAt a b t) (and (specificallyDependsOnAt b a t) (IndependentContinuant a) (not (SpatialRegion a)) (existsAt b t))) // axiom label in BFO2 CLIF: [053-004]
BFO2 Reference: independent continuant that is not a spatial region
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'bearer of at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'bearer of@en'(x,y,t)
BFO2 Reference: specifically dependent continuant
b bearer_of c at t =Def. c s-depends_on b at t & b is an independent continuant that is not a spatial region. (axiom label in BFO2 Reference: [053-004])
bearerOfAt
bearer-of_st
b bearer_of c at t =Def. c s-depends_on b at t & b is an independent continuant that is not a spatial region. (axiom label in BFO2 Reference: [053-004])
(iff (bearerOfAt a b t) (and (specificallyDependsOnAt b a t) (IndependentContinuant a) (not (SpatialRegion a)) (existsAt b t))) // axiom label in BFO2 CLIF: [053-004]
realized in
(forall (x y z t) (if (and (RealizableEntity x) (Process y) (realizesAt y x t) (bearerOfAt z x t)) (hasParticipantAt y z t))) // axiom label in BFO2 CLIF: [106-002]
[copied from inverse property 'realizes'] to say that b realizes c at t is to assert that there is some material entity d & b is a process which has participant d at t & c is a disposition or role of which d is bearer_of at t& the type instantiated by b is correlated with the type instantiated by c. (axiom label in BFO2 Reference: [059-003])
if a realizable entity b is realized in a process p, then p stands in the has_participant relation to the bearer of b. (axiom label in BFO2 Reference: [106-002])
realized-in
realizedIn
if a realizable entity b is realized in a process p, then p stands in the has_participant relation to the bearer of b. (axiom label in BFO2 Reference: [106-002])
(forall (x y z t) (if (and (RealizableEntity x) (Process y) (realizesAt y x t) (bearerOfAt z x t)) (hasParticipantAt y z t))) // axiom label in BFO2 CLIF: [106-002]
realizes
(forall (x y t) (if (realizesAt x y t) (and (Process x) (or (Disposition y) (Role y)) (exists (z) (and (MaterialEntity z) (hasParticipantAt x z t) (bearerOfAt z y t)))))) // axiom label in BFO2 CLIF: [059-003]
realizes
realizes
to say that b realizes c at t is to assert that there is some material entity d & b is a process which has participant d at t & c is a disposition or role of which d is bearer_of at t& the type instantiated by b is correlated with the type instantiated by c. (axiom label in BFO2 Reference: [059-003])
(forall (x y t) (if (realizesAt x y t) (and (Process x) (or (Disposition y) (Role y)) (exists (z) (and (MaterialEntity z) (hasParticipantAt x z t) (bearerOfAt z y t)))))) // axiom label in BFO2 CLIF: [059-003]
to say that b realizes c at t is to assert that there is some material entity d & b is a process which has participant d at t & c is a disposition or role of which d is bearer_of at t& the type instantiated by b is correlated with the type instantiated by c. (axiom label in BFO2 Reference: [059-003])
participates in at some time
[copied from inverse property 'has participant at some time'] BFO2 Reference: process
[copied from inverse property 'has participant at some time'] Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'has participant at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'has participant@en'(x,y,t)
[copied from inverse property 'has participant at some time'] BFO2 Reference: independent continuant that is not a spatial region, specifically dependent continuant, generically dependent continuant
participates-in_st
[copied from inverse property 'has participant at some time'] has_participant is an instance-level relation between a process, a continuant, and a temporal region at which the continuant participates in some way in the process. (axiom label in BFO2 Reference: [086-003])
[copied from inverse property 'has participant at some time'] BFO 2 Reference: Spatial regions do not participate in processes.
participatesInAt
has participant at some time
(forall (x y t) (if (hasParticipantAt x y t) (Continuant y))) // axiom label in BFO2 CLIF: [088-001]
has-participant_st
hasParticipantAt
BFO2 Reference: process
(forall (x y t) (if (hasParticipantAt x y t) (Occurrent x))) // axiom label in BFO2 CLIF: [087-001]
(forall (x y t) (if (hasParticipantAt x y t) (existsAt y t))) // axiom label in BFO2 CLIF: [089-001]
(forall (x y t) (if (and (hasParticipantAt x y t) (GenericallyDependentContinuant y)) (exists (z) (and (IndependentContinuant z) (not (SpatialRegion z)) (genericallyDependsOn y z t) (specificallyDependsOnAt x z t))))) // axiom label in BFO2 CLIF: [091-003]
(forall (x y t) (if (and (hasParticipantAt x y t) (SpecificallyDependentContinuant y)) (exists (z) (and (IndependentContinuant z) (not (SpatialRegion z)) (specificallyDependsOnAt x z t) (specificallyDependsOnAt y z t))))) // axiom label in BFO2 CLIF: [090-003]
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'has participant at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'has participant@en'(x,y,t)
BFO 2 Reference: Spatial regions do not participate in processes.
BFO2 Reference: independent continuant that is not a spatial region, specifically dependent continuant, generically dependent continuant
has_participant is an instance-level relation between a process, a continuant, and a temporal region at which the continuant participates in some way in the process. (axiom label in BFO2 Reference: [086-003])
if b has_participant c at t & c is a generically dependent continuant, then there is some independent continuant that is not a spatial region d, and which is such that c g-depends on d at t & b s-depends_on d at t. (axiom label in BFO2 Reference: [091-003])
if b has_participant c at t & c is a specifically dependent continuant, then there is some independent continuant that is not a spatial region d, c s-depends_on d at t & b s-depends_on d at t. (axiom label in BFO2 Reference: [090-003])
if b has_participant c at t then b is an occurrent. (axiom label in BFO2 Reference: [087-001])
if b has_participant c at t then c exists at t. (axiom label in BFO2 Reference: [089-001])
if b has_participant c at t then c is a continuant. (axiom label in BFO2 Reference: [088-001])
if b has_participant c at t then c exists at t. (axiom label in BFO2 Reference: [089-001])
(forall (x y t) (if (hasParticipantAt x y t) (existsAt y t))) // axiom label in BFO2 CLIF: [089-001]
(forall (x y t) (if (hasParticipantAt x y t) (Occurrent x))) // axiom label in BFO2 CLIF: [087-001]
(forall (x y t) (if (and (hasParticipantAt x y t) (SpecificallyDependentContinuant y)) (exists (z) (and (IndependentContinuant z) (not (SpatialRegion z)) (specificallyDependsOnAt x z t) (specificallyDependsOnAt y z t))))) // axiom label in BFO2 CLIF: [090-003]
(forall (x y t) (if (and (hasParticipantAt x y t) (GenericallyDependentContinuant y)) (exists (z) (and (IndependentContinuant z) (not (SpatialRegion z)) (genericallyDependsOn y z t) (specificallyDependsOnAt x z t))))) // axiom label in BFO2 CLIF: [091-003]
if b has_participant c at t & c is a specifically dependent continuant, then there is some independent continuant that is not a spatial region d, c s-depends_on d at t & b s-depends_on d at t. (axiom label in BFO2 Reference: [090-003])
if b has_participant c at t then c is a continuant. (axiom label in BFO2 Reference: [088-001])
if b has_participant c at t & c is a generically dependent continuant, then there is some independent continuant that is not a spatial region d, and which is such that c g-depends on d at t & b s-depends_on d at t. (axiom label in BFO2 Reference: [091-003])
(forall (x y t) (if (hasParticipantAt x y t) (Continuant y))) // axiom label in BFO2 CLIF: [088-001]
has_participant is an instance-level relation between a process, a continuant, and a temporal region at which the continuant participates in some way in the process. (axiom label in BFO2 Reference: [086-003])
if b has_participant c at t then b is an occurrent. (axiom label in BFO2 Reference: [087-001])
concretized by at some time
concretized-by_st
[copied from inverse property 'concretizes at some time'] you may concretize a poem as a pattern of memory traces in your head
[copied from inverse property 'concretizes at some time'] b concretizes c at t means: b is a specifically dependent continuant & c is a generically dependent continuant & for some independent continuant that is not a spatial region d, b s-depends_on d at t & c g-depends on d at t & if c migrates from bearer d to another bearer e than a copy of b will be created in e. (axiom label in BFO2 Reference: [075-002])
[copied from inverse property 'concretizes at some time'] You may concretize a piece of software by installing it in your computer
[copied from inverse property 'concretizes at some time'] Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'concretizes at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'concretizes@en'(x,y,t)
[copied from inverse property 'concretizes at some time'] You may concretize a recipe that you find in a cookbook by turning it into a plan which exists as a realizable dependent continuant in your head.
concretizes at some time
concretizesAt
(forall (x y t) (if (genericallyDependsOnAt x y t) (exists (z) (and (concretizesAt z x t) (specificallyDependsOnAt z y t))))) // axiom label in BFO2 CLIF: [076-001]
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'concretizes at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'concretizes@en'(x,y,t)
(forall (x y t) (if (concretizesAt x y t) (and (SpecificallyDependentContinuant x) (GenericallyDependentContinuant y) (exists (z) (and (IndependentContinuant z) (specificallyDependsOnAt x z t) (genericallyDependsOnAt y z t)))))) // axiom label in BFO2 CLIF: [075-002]
concretizes_st
You may concretize a piece of software by installing it in your computer
You may concretize a recipe that you find in a cookbook by turning it into a plan which exists as a realizable dependent continuant in your head.
b concretizes c at t means: b is a specifically dependent continuant & c is a generically dependent continuant & for some independent continuant that is not a spatial region d, b s-depends_on d at t & c g-depends on d at t & if c migrates from bearer d to another bearer e than a copy of b will be created in e. (axiom label in BFO2 Reference: [075-002])
if b g-depends on c at some time t, then there is some d, such that d concretizes b at t and d s-depends_on c at t. (axiom label in BFO2 Reference: [076-001])
you may concretize a poem as a pattern of memory traces in your head
(forall (x y t) (if (concretizesAt x y t) (and (SpecificallyDependentContinuant x) (GenericallyDependentContinuant y) (exists (z) (and (IndependentContinuant z) (specificallyDependsOnAt x z t) (genericallyDependsOnAt y z t)))))) // axiom label in BFO2 CLIF: [075-002]
if b g-depends on c at some time t, then there is some d, such that d concretizes b at t and d s-depends_on c at t. (axiom label in BFO2 Reference: [076-001])
b concretizes c at t means: b is a specifically dependent continuant & c is a generically dependent continuant & for some independent continuant that is not a spatial region d, b s-depends_on d at t & c g-depends on d at t & if c migrates from bearer d to another bearer e than a copy of b will be created in e. (axiom label in BFO2 Reference: [075-002])
(forall (x y t) (if (genericallyDependsOnAt x y t) (exists (z) (and (concretizesAt z x t) (specificallyDependsOnAt z y t))))) // axiom label in BFO2 CLIF: [076-001]
occurs in
occursIn
b occurs_in c =def b is a process and c is a material entity or immaterial entity& there exists a spatiotemporal region r and b occupies_spatiotemporal_region r.& forall(t) if b exists_at t then c exists_at t & there exist spatial regions s and s’ where & b spatially_projects_onto s at t& c is occupies_spatial_region s’ at t& s is a proper_continuant_part_of s’ at t [XXX-001
occurs-in
contains process
contains-process
containsProcess
[copied from inverse property 'occurs in'] b occurs_in c =def b is a process and c is a material entity or immaterial entity& there exists a spatiotemporal region r and b occupies_spatiotemporal_region r.& forall(t) if b exists_at t then c exists_at t & there exist spatial regions s and s’ where & b spatially_projects_onto s at t& c is occupies_spatial_region s’ at t& s is a proper_continuant_part_of s’ at t [XXX-001
specifically depends on at all times
(forall (x y t) (if (and (Entity x) (or (continuantPartOfAt y x t) (continuantPartOfAt x y t) (occurrentPartOf x y) (occurrentPartOf y x))) (not (specificallyDependsOnAt x y t)))) // axiom label in BFO2 CLIF: [013-002]
(forall (x y z t) (if (and (specificallyDependsOnAt x y t) (specificallyDependsOnAt y z t)) (specificallyDependsOnAt x z t))) // axiom label in BFO2 CLIF: [054-002]
specificallyDependsOn
(forall (x y t) (if (and (Occurrent x) (IndependentContinuant y) (specificallyDependsOnAt x y t)) (forall (t_1) (if (existsAt x t_1) (specificallyDependsOnAt x y t_1))))) // axiom label in BFO2 CLIF: [015-002]
A pain s-depends_on the organism that is experiencing the pain
BFO2 Reference: specifically dependent continuant\; process; process boundary
s-depends-on_at
(forall (x) (if (exists (y t) (specificallyDependsOnAt x y t)) (not (MaterialEntity x)))) // axiom label in BFO2 CLIF: [052-001]
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'specifically depends on at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'specifically depends on@en(x,y,t)'.
(forall (x y t) (if (specificallyDependsOnAt x y t) (exists (z) (and (IndependentContinuant z) (not (SpatialRegion z)) (specificallyDependsOnAt x z t))))) // axiom label in BFO2 CLIF: [136-001]
BFO 2 Reference: An entity – for example an act of communication or a game of football – can s-depends_on more than one entity. Complex phenomena for example in the psychological and social realms (such as inferring, commanding and requesting) or in the realm of multi-organismal biological processes (such as infection and resistance), will involve multiple families of dependence relations, involving both continuants and occurrents [1, 4, 28
BFO 2 Reference: S-dependence is just one type of dependence among many; it is what, in the literature, is referred to as ‘existential dependence’ [87, 46, 65, 20
BFO 2 Reference: the relation of s-depends_on does not in every case require simultaneous existence of its relata. Note the difference between such cases and the cases of continuant universals defined historically: the act of answering depends existentially on the prior act of questioning; the human being who was baptized or who answered a question does not himself depend existentially on the prior act of baptism or answering. He would still exist even if these acts had never taken place.
If b is s-depends_on something at some time, then b is not a material entity. (axiom label in BFO2 Reference: [052-001])
If b s-depends_on something at t, then there is some c, which is an independent continuant and not a spatial region, such that b s-depends_on c at t. (axiom label in BFO2 Reference: [136-001])
If occurrent b s-depends_on some independent continuant c at t, then b s-depends_on c at every time at which b exists. (axiom label in BFO2 Reference: [015-002])
To say that b s-depends_on a at t is to say that b and c do not share common parts & b is of its nature such that it cannot exist unless c exists & b is not a boundary of c and b is not a site of which c is the host [64
a gait s-depends_on the walking object. (All at some specific time.)
a shape s-depends_on the shaped object
an entity does not s-depend_on any of its (continuant or occurrent) parts or on anything it is part of. (axiom label in BFO2 Reference: [013-002])
if b s-depends_on c at t & c s-depends_on d at t then b s-depends_on d at t. (axiom label in BFO2 Reference: [054-002])
one-sided s-dependence of a dependent continuant on an independent continuant: an instance of headache s-depends_on some head
one-sided s-dependence of a dependent continuant on an independent continuant: an instance of temperature s-depends_on some organism
one-sided s-dependence of a process on something: a process of cell death s-depends_on a cell
one-sided s-dependence of a process on something: an instance of seeing (a relational process) s-depends_on some organism and on some seen entity, which may be an occurrent or a continuant
one-sided s-dependence of one occurrent on another: a process of answering a question is dependent on a prior process of asking a question
one-sided s-dependence of one occurrent on another: a process of obeying a command is dependent on a prior process of issuing a command
one-sided s-dependence of one occurrent on multiple independent continuants: a relational process of hitting a ball with a cricket bat
one-sided s-dependence of one occurrent on multiple independent continuants: a relational process of paying cash to a merchant in exchange for a bag of figs
reciprocal s-dependence between occurrents: a process of buying and the associated process of selling
reciprocal s-dependence between occurrents: a process of increasing the volume of a portion of gas while temperature remains constant and the associated process of decreasing the pressure exerted by the gas
reciprocal s-dependence between occurrents: in a game of chess the process of playing with the white pieces is mutually dependent on the process of playing with the black pieces
the one-sided dependence of an occurrent on an independent continuant: football match on the players, the ground, the ball
the one-sided dependence of an occurrent on an independent continuant: handwave on a hand
the three-sided reciprocal s-dependence of the hue, saturation and brightness of a color [45
the three-sided reciprocal s-dependence of the pitch, timbre and volume of a tone [45
the two-sided reciprocal s-dependence of the roles of husband and wife [20
if b s-depends_on c at t & c s-depends_on d at t then b s-depends_on d at t. (axiom label in BFO2 Reference: [054-002])
(forall (x y t) (if (specificallyDependsOnAt x y t) (exists (z) (and (IndependentContinuant z) (not (SpatialRegion z)) (specificallyDependsOnAt x z t))))) // axiom label in BFO2 CLIF: [136-001]
(forall (x y t) (if (and (Entity x) (or (continuantPartOfAt y x t) (continuantPartOfAt x y t) (occurrentPartOf x y) (occurrentPartOf y x))) (not (specificallyDependsOnAt x y t)))) // axiom label in BFO2 CLIF: [013-002]
(forall (x y z t) (if (and (specificallyDependsOnAt x y t) (specificallyDependsOnAt y z t)) (specificallyDependsOnAt x z t))) // axiom label in BFO2 CLIF: [054-002]
(forall (x) (if (exists (y t) (specificallyDependsOnAt x y t)) (not (MaterialEntity x)))) // axiom label in BFO2 CLIF: [052-001]
If occurrent b s-depends_on some independent continuant c at t, then b s-depends_on c at every time at which b exists. (axiom label in BFO2 Reference: [015-002])
If b s-depends_on something at t, then there is some c, which is an independent continuant and not a spatial region, such that b s-depends_on c at t. (axiom label in BFO2 Reference: [136-001])
an entity does not s-depend_on any of its (continuant or occurrent) parts or on anything it is part of. (axiom label in BFO2 Reference: [013-002])
If b is s-depends_on something at some time, then b is not a material entity. (axiom label in BFO2 Reference: [052-001])
(forall (x y t) (if (and (Occurrent x) (IndependentContinuant y) (specificallyDependsOnAt x y t)) (forall (t_1) (if (existsAt x t_1) (specificallyDependsOnAt x y t_1))))) // axiom label in BFO2 CLIF: [015-002]
function of at all times
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'function of at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'function of@en(x,y,t)'.
f-of_at
(iff (functionOf a b t) (and (Function a) (inheresInAt a b t))) // axiom label in BFO2 CLIF: [067-001]
functionOfAt
a function_of b at t =Def. a is a function and a inheres_in b at t. (axiom label in BFO2 Reference: [067-001])
a function_of b at t =Def. a is a function and a inheres_in b at t. (axiom label in BFO2 Reference: [067-001])
(iff (functionOf a b t) (and (Function a) (inheresInAt a b t))) // axiom label in BFO2 CLIF: [067-001]
quality of at all times
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'quality of at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'quality of@en(x,y,t)'.
b quality_of c at t = Def. b is a quality & c is an independent continuant that is not a spatial region & b s-depends_on c at t. (axiom label in BFO2 Reference: [056-002])
q-of_at
(iff (qualityOfAt a b t) (and (Quality a) (IndependentContinuant b) (not (SpatialRegion b)) (specificallyDependsOnAt a b t))) // axiom label in BFO2 CLIF: [056-002]
qualityOfAt
b quality_of c at t = Def. b is a quality & c is an independent continuant that is not a spatial region & b s-depends_on c at t. (axiom label in BFO2 Reference: [056-002])
(iff (qualityOfAt a b t) (and (Quality a) (IndependentContinuant b) (not (SpatialRegion b)) (specificallyDependsOnAt a b t))) // axiom label in BFO2 CLIF: [056-002]
role of at all times
roleOfAt
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'role of at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'role of@en(x,y,t)'.
(iff (roleOfAt a b t) (and (Role a) (inheresInAt a b t))) // axiom label in BFO2 CLIF: [065-001]
a role_of b at t =Def. a is a role and a inheres_in b at t. (axiom label in BFO2 Reference: [065-001])
r-of_at
(iff (roleOfAt a b t) (and (Role a) (inheresInAt a b t))) // axiom label in BFO2 CLIF: [065-001]
a role_of b at t =Def. a is a role and a inheres_in b at t. (axiom label in BFO2 Reference: [065-001])
located in at all times
located-in_at
(forall (x y z t) (if (and (IndependentContinuant x) (IndependentContinuant y) (IndependentContinuant z) (locatedInAt x y t) (continuantPartOfAt y z t)) (locatedInAt x z t))) // axiom label in BFO2 CLIF: [049-001]
locatedInAt
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'located in at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'located in@en(x,y,t)'.
(iff (locatedInAt a b t) (and (IndependentContinuant a) (IndependentContinuant b) (exists (r_1 r_2) (and (occupiesSpatialRegionAt a r_1 t) (occupiesSpatialRegionAt b r_2 t) (continuantPartOfAt r_1 r_2 t))))) // axiom label in BFO2 CLIF: [045-001]
BFO2 Reference: independent continuant
(forall (x y z t) (if (and (IndependentContinuant x) (IndependentContinuant y) (IndependentContinuant z) (continuantPartOfAt x y t) (locatedInAt y z t)) (locatedInAt x z t))) // axiom label in BFO2 CLIF: [048-001]
(forall (x y z t) (if (and (locatedInAt x y t) (locatedInAt y z t)) (locatedInAt x z t))) // axiom label in BFO2 CLIF: [046-001]
Located_in is transitive. (axiom label in BFO2 Reference: [046-001])
Mary located_in Salzburg
b located_in c at t = Def. b and c are independent continuants, and the region at which b is located at t is a (proper or improper) continuant_part_of the region at which c is located at t. (axiom label in BFO2 Reference: [045-001])
for all independent continuants b, c, and d: if b continuant_part_of c at t & c located_in d at t, then b located_in d at t. (axiom label in BFO2 Reference: [048-001])
for all independent continuants b, c, and d: if b located_in c at t & c continuant_part_of d at t, then b located_in d at t. (axiom label in BFO2 Reference: [049-001])
the Empire State Building located_in New York.
this portion of cocaine located_in this portion of blood
this stem cell located_in this portion of bone marrow
your arm located_in your body
for all independent continuants b, c, and d: if b continuant_part_of c at t & c located_in d at t, then b located_in d at t. (axiom label in BFO2 Reference: [048-001])
for all independent continuants b, c, and d: if b located_in c at t & c continuant_part_of d at t, then b located_in d at t. (axiom label in BFO2 Reference: [049-001])
(forall (x y z t) (if (and (IndependentContinuant x) (IndependentContinuant y) (IndependentContinuant z) (continuantPartOfAt x y t) (locatedInAt y z t)) (locatedInAt x z t))) // axiom label in BFO2 CLIF: [048-001]
(forall (x y z t) (if (and (IndependentContinuant x) (IndependentContinuant y) (IndependentContinuant z) (locatedInAt x y t) (continuantPartOfAt y z t)) (locatedInAt x z t))) // axiom label in BFO2 CLIF: [049-001]
b located_in c at t = Def. b and c are independent continuants, and the region at which b is located at t is a (proper or improper) continuant_part_of the region at which c is located at t. (axiom label in BFO2 Reference: [045-001])
Located_in is transitive. (axiom label in BFO2 Reference: [046-001])
(forall (x y z t) (if (and (locatedInAt x y t) (locatedInAt y z t)) (locatedInAt x z t))) // axiom label in BFO2 CLIF: [046-001]
(iff (locatedInAt a b t) (and (IndependentContinuant a) (IndependentContinuant b) (exists (r_1 r_2) (and (occupiesSpatialRegionAt a r_1 t) (occupiesSpatialRegionAt b r_2 t) (continuantPartOfAt r_1 r_2 t))))) // axiom label in BFO2 CLIF: [045-001]
occupies spatial region at some time
occupiesSpatialRegionAt
(forall (r t) (if (Region r) (occupiesSpatialRegionAt r r t))) // axiom label in BFO2 CLIF: [042-002]
BFO2 Reference: spatial region
located-at-r_st
(forall (x y r_1 t) (if (and (occupiesSpatialRegionAt x r_1 t) (continuantPartOfAt y x t)) (exists (r_2) (and (continuantPartOfAt r_2 r_1 t) (occupiesSpatialRegionAt y r_2 t))))) // axiom label in BFO2 CLIF: [043-001]
(forall (x r t) (if (occupiesSpatialRegionAt x r t) (and (SpatialRegion r) (IndependentContinuant x)))) // axiom label in BFO2 CLIF: [041-002]
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'occupies spatial region at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'occupies spatial region@en'(x,y,t)
BFO2 Reference: independent continuant
b occupies_spatial_region r at t means that r is a spatial region in which independent continuant b is exactly located (axiom label in BFO2 Reference: [041-002])
every region r is occupies_spatial_region r at all times. (axiom label in BFO2 Reference: [042-002])
if b occupies_spatial_region r at t & b continuant_part_of b at t, then there is some r which is continuant_part_of r at t such that b occupies_spatial_region r at t. (axiom label in BFO2 Reference: [043-001])
b occupies_spatial_region r at t means that r is a spatial region in which independent continuant b is exactly located (axiom label in BFO2 Reference: [041-002])
(forall (x y r_1 t) (if (and (occupiesSpatialRegionAt x r_1 t) (continuantPartOfAt y x t)) (exists (r_2) (and (continuantPartOfAt r_2 r_1 t) (occupiesSpatialRegionAt y r_2 t))))) // axiom label in BFO2 CLIF: [043-001]
(forall (x r t) (if (occupiesSpatialRegionAt x r t) (and (SpatialRegion r) (IndependentContinuant x)))) // axiom label in BFO2 CLIF: [041-002]
every region r is occupies_spatial_region r at all times. (axiom label in BFO2 Reference: [042-002])
(forall (r t) (if (Region r) (occupiesSpatialRegionAt r r t))) // axiom label in BFO2 CLIF: [042-002]
if b occupies_spatial_region r at t & b continuant_part_of b at t, then there is some r which is continuant_part_of r at t such that b occupies_spatial_region r at t. (axiom label in BFO2 Reference: [043-001])
generically depends on at some time
genericallyDependsOn
g-depends-on_st
BFO2 Reference: generically dependent continuant
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'generically depends on at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'generically depends on@en'(x,y,t)
(forall (x y) (if (exists (t) (genericallyDependsOnAt x y t)) (forall (t_1) (if (existsAt x t_1) (exists (z) (genericallyDependsOnAt x z t_1)))))) // axiom label in BFO2 CLIF: [073-001]
BFO2 Reference: independent continuant
b g-depends on c at t1 means: b exists at t1 and c exists at t1 & for some type B it holds that (c instantiates B at t1) & necessarily, for all t (if b exists at t then some instance_of B exists at t) & not (b s-depends_on c at t1). (axiom label in BFO2 Reference: [072-002])
if b g-depends_on c at some time t, then b g-depends_on something at all times at which b exists. (axiom label in BFO2 Reference: [073-001])
(forall (x y) (if (exists (t) (genericallyDependsOnAt x y t)) (forall (t_1) (if (existsAt x t_1) (exists (z) (genericallyDependsOnAt x z t_1)))))) // axiom label in BFO2 CLIF: [073-001]
b g-depends on c at t1 means: b exists at t1 and c exists at t1 & for some type B it holds that (c instantiates B at t1) & necessarily, for all t (if b exists at t then some instance_of B exists at t) & not (b s-depends_on c at t1). (axiom label in BFO2 Reference: [072-002])
if b g-depends_on c at some time t, then b g-depends_on something at all times at which b exists. (axiom label in BFO2 Reference: [073-001])
has function at some time
hasFunctionAt
(iff (hasFunctionAt a b t) (functionOf b a t)) // axiom label in BFO2 CLIF: [070-001]
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'has function at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'has function@en'(x,y,t)
a has_function b at t =Def. b function_of a at t. (axiom label in BFO2 Reference: [070-001])
has-f_st
(iff (hasFunctionAt a b t) (functionOf b a t)) // axiom label in BFO2 CLIF: [070-001]
a has_function b at t =Def. b function_of a at t. (axiom label in BFO2 Reference: [070-001])
has quality at some time
has-q_st
has role at some time
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'has role at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'has role@en'(x,y,t)
a has_role b at t =Def. b role_of a at t. (axiom label in BFO2 Reference: [068-001])
hasRoleAt
(iff (hasRoleAt a b t) (roleOfAt b a t)) // axiom label in BFO2 CLIF: [068-001]
has-r_st
(iff (hasRoleAt a b t) (roleOfAt b a t)) // axiom label in BFO2 CLIF: [068-001]
a has_role b at t =Def. b role_of a at t. (axiom label in BFO2 Reference: [068-001])
has generic dependent at some time
[copied from inverse property 'generically depends on at some time'] BFO2 Reference: independent continuant
has-g-dep_st
[copied from inverse property 'generically depends on at some time'] b g-depends on c at t1 means: b exists at t1 and c exists at t1 & for some type B it holds that (c instantiates B at t1) & necessarily, for all t (if b exists at t then some instance_of B exists at t) & not (b s-depends_on c at t1). (axiom label in BFO2 Reference: [072-002])
[copied from inverse property 'generically depends on at some time'] BFO2 Reference: generically dependent continuant
[copied from inverse property 'generically depends on at some time'] Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'generically depends on at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'generically depends on@en'(x,y,t)
disposition of at all times
(iff (dispositionOf a b t) (and (Disposition a) (inheresInAt a b t))) // axiom label in BFO2 CLIF: [066-001]
dispositionOfAt
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'disposition of at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'disposition of@en(x,y,t)'.
a disposition_of b at t =Def. a is a disposition and a inheres_in b at t. (axiom label in BFO2 Reference: [066-001])
d-of_at
a disposition_of b at t =Def. a is a disposition and a inheres_in b at t. (axiom label in BFO2 Reference: [066-001])
(iff (dispositionOf a b t) (and (Disposition a) (inheresInAt a b t))) // axiom label in BFO2 CLIF: [066-001]
exists at
exists-at
existsAt
BFO2 Reference: entity
BFO2 Reference: temporal region
b exists_at t means: b is an entity which exists at some temporal region t. (axiom label in BFO2 Reference: [118-002])
b exists_at t means: b is an entity which exists at some temporal region t. (axiom label in BFO2 Reference: [118-002])
has continuant part at all times
hasContinuantPartAt
(iff (hasContinuantPartAt a b t) (continuantPartOfAt b a t)) // axiom label in BFO2 CLIF: [006-001]
b has_continuant_part c at t = Def. c continuant_part_of b at t. (axiom label in BFO2 Reference: [006-001])
c-has-part_at
[copied from inverse property 'part of continuant at all times that whole exists'] forall(t) exists_at(y,t) -> exists_at(x,t) and 'part of continuant'(x,y,t)
[copied from inverse property 'part of continuant at all times that whole exists'] This is a binary version of a ternary time-indexed, instance level, relation. Unlike the rest of the temporalized relations which temporally quantify over existence of the subject of the relation, this relation temporally quantifies over the existence of the object of the relation. The relation is provided tentatively, to assess whether the GO needs such a relation. It is inverse of 'has continuant part at all times'
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'has continuant part at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'has continuant part@en(x,y,t)'.
b has_continuant_part c at t = Def. c continuant_part_of b at t. (axiom label in BFO2 Reference: [006-001])
(iff (hasContinuantPartAt a b t) (continuantPartOfAt b a t)) // axiom label in BFO2 CLIF: [006-001]
has proper continuant part at all times
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'has proper continuant part at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'has proper continuant part@en(x,y,t)'.
hasProperContinuantPartAt
c-has-ppart_at
b has_proper_continuant_part c at t = Def. c proper_continuant_part_of b at t. [XXX-001
has disposition at some time
has-d_st
hasDispositionAt
(iff (hasDispositionAt a b t) (dispositionOf b a t)) // axiom label in BFO2 CLIF: [069-001]
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'has disposition at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'has disposition@en'(x,y,t)
a has_disposition b at t =Def. b disposition_of a at t. (axiom label in BFO2 Reference: [069-001])
(iff (hasDispositionAt a b t) (dispositionOf b a t)) // axiom label in BFO2 CLIF: [069-001]
a has_disposition b at t =Def. b disposition_of a at t. (axiom label in BFO2 Reference: [069-001])
has material basis at all times
has-material-basis_at
hasMaterialBasisAt
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'has material basis at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'has material basis@en(x,y,t)'.
(forall (x y t) (if (hasMaterialBasisAt x y t) (and (Disposition x) (MaterialEntity y) (exists (z) (and (bearerOfAt z x t) (continuantPartOfAt y z t) (exists (w) (and (Disposition w) (if (hasDisposition z w) (continuantPartOfAt y z t))))))))) // axiom label in BFO2 CLIF: [071-002]
b has_material_basis c at t means: b is a disposition & c is a material entity & there is some d bearer_of b at t& c continuant_part_of d at t& d has_disposition b at t because c continuant_part_of d at t. (axiom label in BFO2 Reference: [071-002])
the material basis of John’s disposition to cough is the viral infection in John’s upper respiratory tract
the material basis of the disposition to wear unevenly of John’s tires is the worn suspension of his car.
(forall (x y t) (if (hasMaterialBasisAt x y t) (and (Disposition x) (MaterialEntity y) (exists (z) (and (bearerOfAt z x t) (continuantPartOfAt y z t) (exists (w) (and (Disposition w) (if (hasDisposition z w) (continuantPartOfAt y z t))))))))) // axiom label in BFO2 CLIF: [071-002]
b has_material_basis c at t means: b is a disposition & c is a material entity & there is some d bearer_of b at t& c continuant_part_of d at t& d has_disposition b at t because c continuant_part_of d at t. (axiom label in BFO2 Reference: [071-002])
has member part at some time
[copied from inverse property 'member part of at some time'] BFO2 Reference: object
[copied from inverse property 'member part of at some time'] Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'member part of at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'member part of@en'(x,y,t)
[copied from inverse property 'member part of at some time'] each piece in a chess set is a member part of the chess set; each Beatle in the collection called The Beatles is a member part of The Beatles.
[copied from inverse property 'member part of at some time'] b member_part_of c at t =Def. b is an object & there is at t a mutually exhaustive and pairwise disjoint partition of c into objects x1, …, xn (for some n > 1) with b = xi for some 1 ? i ? n. (axiom label in BFO2 Reference: [026-004])
[copied from inverse property 'member part of at some time'] each tree in a forest is a member_part of the forest
has-member-part_st
[copied from inverse property 'member part of at some time'] BFO2 Reference: object aggregate
has occurrent part
[copied from inverse property 'part of occurrent'] Mary’s 5th birthday occurrent_part_of Mary’s life
[copied from inverse property 'part of occurrent'] the first set of the tennis match occurrent_part_of the tennis match.
[copied from inverse property 'part of occurrent'] BFO 2 Reference: a (continuant or occurrent) part of itself. We appreciate that this is counterintuitive for some users, since it implies for example that President Obama is a part of himself. However it brings benefits in simplifying the logical formalism, and it captures an important feature of identity, namely that it is the limit case of mereological inclusion.
(iff (hasOccurrentPart a b) (occurrentPartOf b a)) // axiom label in BFO2 CLIF: [007-001]
[copied from inverse property 'part of occurrent'] BFO2 Reference: occurrent
o-has-part
hasOccurrentPart
[copied from inverse property 'part of occurrent'] b occurrent_part_of c =Def. b is a part of c & b and c are occurrents. (axiom label in BFO2 Reference: [003-002])
[copied from inverse property 'part of occurrent'] The process of a footballer’s heart beating once is an occurrent part but not a temporal_part of a game of football.
b has_occurrent_part c = Def. c occurrent_part_of b. (axiom label in BFO2 Reference: [007-001])
(iff (hasOccurrentPart a b) (occurrentPartOf b a)) // axiom label in BFO2 CLIF: [007-001]
b has_occurrent_part c = Def. c occurrent_part_of b. (axiom label in BFO2 Reference: [007-001])
has proper occurrent part
[copied from inverse property 'proper part of occurrent'] b proper_occurrent_part_of c =Def. b occurrent_part_of c & b and c are not identical. (axiom label in BFO2 Reference: [005-001])
hasProperOccurrentPart
o-has-ppart
b has_proper_occurrent_part c = Def. c proper_occurrent_part_of b. [XXX-001
has profile
has-profile
has temporal part
[copied from inverse property 'temporal part of'] the 4th year of your life is a temporal part of your life\. The first quarter of a game of football is a temporal part of the whole game\. The process of your heart beating from 4pm to 5pm today is a temporal part of the entire process of your heart beating.\ The 4th year of your life is a temporal part of your life
[copied from inverse property 'temporal part of'] your heart beating from 4pm to 5pm today is a temporal part of the process of your heart beating
[copied from inverse property 'temporal part of'] the process boundary which separates the 3rd and 4th years of your life.
[copied from inverse property 'temporal part of'] b proper_temporal_part_of c =Def. b temporal_part_of c & not (b = c). (axiom label in BFO2 Reference: [116-001])
has-t-part
[copied from inverse property 'temporal part of'] b temporal_part_of c =Def.b occurrent_part_of c & & for some temporal region t, b occupies_temporal_region t & for all occurrents d, t (if d occupies_temporal_region t & t? occurrent_part_of t then (d occurrent_part_of a iff d occurrent_part_of b)). (axiom label in BFO2 Reference: [078-003])
has spatial occupant at some time
r-location-of_st
[copied from inverse property 'occupies spatial region at some time'] BFO2 Reference: independent continuant
[copied from inverse property 'occupies spatial region at some time'] b occupies_spatial_region r at t means that r is a spatial region in which independent continuant b is exactly located (axiom label in BFO2 Reference: [041-002])
[copied from inverse property 'occupies spatial region at some time'] Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'occupies spatial region at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'occupies spatial region@en'(x,y,t)
[copied from inverse property 'occupies spatial region at some time'] BFO2 Reference: spatial region
has location at some time
[copied from inverse property 'located in at some time'] Mary located_in Salzburg
has-location_st
[copied from inverse property 'located in at some time'] your arm located_in your body
[copied from inverse property 'located in at some time'] Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'located in at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'located in@en'(x,y,t)
[copied from inverse property 'located in at some time'] BFO2 Reference: independent continuant
[copied from inverse property 'located in at some time'] this portion of cocaine located_in this portion of blood
[copied from inverse property 'located in at some time'] this stem cell located_in this portion of bone marrow
[copied from inverse property 'located in at some time'] b located_in c at t = Def. b and c are independent continuants, and the region at which b is located at t is a (proper or improper) continuant_part_of the region at which c is located at t. (axiom label in BFO2 Reference: [045-001])
[copied from inverse property 'located in at some time'] the Empire State Building located_in New York.
has specific dependent at some time
[copied from inverse property 'specifically depends on at some time'] reciprocal s-dependence between occurrents: a process of increasing the volume of a portion of gas while temperature remains constant and the associated process of decreasing the pressure exerted by the gas
[copied from inverse property 'specifically depends on at some time'] one-sided s-dependence of one occurrent on multiple independent continuants: a relational process of hitting a ball with a cricket bat
[copied from inverse property 'specifically depends on at some time'] one-sided s-dependence of one occurrent on multiple independent continuants: a relational process of paying cash to a merchant in exchange for a bag of figs
[copied from inverse property 'specifically depends on at some time'] the one-sided dependence of an occurrent on an independent continuant: football match on the players, the ground, the ball
has-s-dep_st
[copied from inverse property 'specifically depends on at some time'] BFO 2 Reference: S-dependence is just one type of dependence among many; it is what, in the literature, is referred to as ‘existential dependence’ [87, 46, 65, 20
[copied from inverse property 'specifically depends on at some time'] a shape s-depends_on the shaped object
[copied from inverse property 'specifically depends on at some time'] one-sided s-dependence of a dependent continuant on an independent continuant: an instance of headache s-depends_on some head
[copied from inverse property 'specifically depends on at some time'] the three-sided reciprocal s-dependence of the pitch, timbre and volume of a tone [45
[copied from inverse property 'specifically depends on at some time'] one-sided s-dependence of a process on something: an instance of seeing (a relational process) s-depends_on some organism and on some seen entity, which may be an occurrent or a continuant
[copied from inverse property 'specifically depends on at some time'] a gait s-depends_on the walking object. (All at some specific time.)
[copied from inverse property 'specifically depends on at some time'] To say that b s-depends_on a at t is to say that b and c do not share common parts & b is of its nature such that it cannot exist unless c exists & b is not a boundary of c and b is not a site of which c is the host [64
[copied from inverse property 'specifically depends on at some time'] BFO 2 Reference: the relation of s-depends_on does not in every case require simultaneous existence of its relata. Note the difference between such cases and the cases of continuant universals defined historically: the act of answering depends existentially on the prior act of questioning; the human being who was baptized or who answered a question does not himself depend existentially on the prior act of baptism or answering. He would still exist even if these acts had never taken place.
[copied from inverse property 'specifically depends on at some time'] reciprocal s-dependence between occurrents: in a game of chess the process of playing with the white pieces is mutually dependent on the process of playing with the black pieces
[copied from inverse property 'specifically depends on at some time'] the three-sided reciprocal s-dependence of the hue, saturation and brightness of a color [45
[copied from inverse property 'specifically depends on at some time'] Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'specifically depends on at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'specifically depends on@en'(x,y,t)
[copied from inverse property 'specifically depends on at some time'] reciprocal s-dependence between occurrents: a process of buying and the associated process of selling
[copied from inverse property 'specifically depends on at some time'] one-sided s-dependence of one occurrent on another: a process of answering a question is dependent on a prior process of asking a question
[copied from inverse property 'specifically depends on at some time'] one-sided s-dependence of one occurrent on another: a process of obeying a command is dependent on a prior process of issuing a command
[copied from inverse property 'specifically depends on at some time'] BFO 2 Reference: An entity – for example an act of communication or a game of football – can s-depends_on more than one entity. Complex phenomena for example in the psychological and social realms (such as inferring, commanding and requesting) or in the realm of multi-organismal biological processes (such as infection and resistance), will involve multiple families of dependence relations, involving both continuants and occurrents [1, 4, 28
[copied from inverse property 'specifically depends on at some time'] A pain s-depends_on the organism that is experiencing the pain
[copied from inverse property 'specifically depends on at some time'] the one-sided dependence of an occurrent on an independent continuant: handwave on a hand
[copied from inverse property 'specifically depends on at some time'] the two-sided reciprocal s-dependence of the roles of husband and wife [20
[copied from inverse property 'specifically depends on at some time'] one-sided s-dependence of a process on something: a process of cell death s-depends_on a cell
[copied from inverse property 'specifically depends on at some time'] BFO2 Reference: specifically dependent continuant\; process; process boundary
[copied from inverse property 'specifically depends on at some time'] one-sided s-dependence of a dependent continuant on an independent continuant: an instance of temperature s-depends_on some organism
has spatiotemporal occupant
occupied-by
[copied from inverse property 'occupies spatiotemporal region'] BFO 2 Reference: The occupies_spatiotemporal_region and occupies_temporal_region relations are the counterpart, on the occurrent side, of the relation occupies_spatial_region.
[copied from inverse property 'occupies spatiotemporal region'] p occupies_spatiotemporal_region s. This is a primitive relation between an occurrent p and the spatiotemporal region s which is its spatiotemporal extent. (axiom label in BFO2 Reference: [082-003])
material basis of at some time
material-basis-of_st
member part of at some time
BFO2 Reference: object aggregate
member-part-of_st
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'member part of at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'member part of@en'(x,y,t)
(forall (x y t) (if (memberPartOfAt x y t) (continuantPartOfAt x y t))) // axiom label in BFO2 CLIF: [104-001]
BFO2 Reference: object
b member_part_of c at t =Def. b is an object & there is at t a mutually exhaustive and pairwise disjoint partition of c into objects x1, …, xn (for some n > 1) with b = xi for some 1 ? i ? n. (axiom label in BFO2 Reference: [026-004])
each piece in a chess set is a member part of the chess set; each Beatle in the collection called The Beatles is a member part of The Beatles.
each tree in a forest is a member_part of the forest
if b member_part_of c at t then b continuant_part_of c at t. (axiom label in BFO2 Reference: [104-001])
memberPartOfAt
b member_part_of c at t =Def. b is an object & there is at t a mutually exhaustive and pairwise disjoint partition of c into objects x1, …, xn (for some n > 1) with b = xi for some 1 ? i ? n. (axiom label in BFO2 Reference: [026-004])
if b member_part_of c at t then b continuant_part_of c at t. (axiom label in BFO2 Reference: [104-001])
(forall (x y t) (if (memberPartOfAt x y t) (continuantPartOfAt x y t))) // axiom label in BFO2 CLIF: [104-001]
occupies spatiotemporal region
occupies
BFO 2 Reference: The occupies_spatiotemporal_region and occupies_temporal_region relations are the counterpart, on the occurrent side, of the relation occupies_spatial_region.
occupiesSpatiotemporalRegion
p occupies_spatiotemporal_region s. This is a primitive relation between an occurrent p and the spatiotemporal region s which is its spatiotemporal extent. (axiom label in BFO2 Reference: [082-003])
p occupies_spatiotemporal_region s. This is a primitive relation between an occurrent p and the spatiotemporal region s which is its spatiotemporal extent. (axiom label in BFO2 Reference: [082-003])
part of occurrent
[copied from inverse property 'has occurrent part'] b has_occurrent_part c = Def. c occurrent_part_of b. (axiom label in BFO2 Reference: [007-001])
BFO2 Reference: occurrent
(forall (x) (if (Occurrent x) (occurrentPartOf x x))) // axiom label in BFO2 CLIF: [113-002]
(forall (x y t) (if (and (occurrentPartOf x y t) (occurrentPartOf y x t)) (= x y))) // axiom label in BFO2 CLIF: [123-001]
occurrentPartOf
(forall (x y z) (if (and (occurrentPartOf x y) (occurrentPartOf y z)) (occurrentPartOf x z))) // axiom label in BFO2 CLIF: [112-001]
o-part-of
(forall (x y t) (if (exists (v) (and (occurrentPartOf v x t) (occurrentPartOf v y t))) (exists (z) (forall (u w) (iff (iff (occurrentPartOf w u t) (and (occurrentPartOf w x t) (occurrentPartOf w y t))) (= z u)))))) // axiom label in BFO2 CLIF: [125-001]
(forall (x y t) (if (and (occurrentPartOf x y t) (not (= x y))) (exists (z) (and (occurrentPartOf z y t) (not (exists (w) (and (occurrentPartOf w x t) (occurrentPartOf w z t)))))))) // axiom label in BFO2 CLIF: [124-001]
BFO 2 Reference: a (continuant or occurrent) part of itself. We appreciate that this is counterintuitive for some users, since it implies for example that President Obama is a part of himself. However it brings benefits in simplifying the logical formalism, and it captures an important feature of identity, namely that it is the limit case of mereological inclusion.
Mary’s 5th birthday occurrent_part_of Mary’s life
The process of a footballer’s heart beating once is an occurrent part but not a temporal_part of a game of football.
b occurrent_part_of c =Def. b is a part of c & b and c are occurrents. (axiom label in BFO2 Reference: [003-002])
occurrent_part_of is antisymmetric. (axiom label in BFO2 Reference: [123-001])
occurrent_part_of is reflexive (every occurrent entity is an occurrent_part_of itself). (axiom label in BFO2 Reference: [113-002])
occurrent_part_of is transitive. (axiom label in BFO2 Reference: [112-001])
occurrent_part_of satisfies unique product. (axiom label in BFO2 Reference: [125-001])
occurrent_part_of satisfies weak supplementation. (axiom label in BFO2 Reference: [124-001])
the first set of the tennis match occurrent_part_of the tennis match.
(forall (x y z) (if (and (occurrentPartOf x y) (occurrentPartOf y z)) (occurrentPartOf x z))) // axiom label in BFO2 CLIF: [112-001]
occurrent_part_of satisfies unique product. (axiom label in BFO2 Reference: [125-001])
(forall (x y t) (if (exists (v) (and (occurrentPartOf v x t) (occurrentPartOf v y t))) (exists (z) (forall (u w) (iff (iff (occurrentPartOf w u t) (and (occurrentPartOf w x t) (occurrentPartOf w y t))) (= z u)))))) // axiom label in BFO2 CLIF: [125-001]
occurrent_part_of is transitive. (axiom label in BFO2 Reference: [112-001])
(forall (x y t) (if (and (occurrentPartOf x y t) (occurrentPartOf y x t)) (= x y))) // axiom label in BFO2 CLIF: [123-001]
(forall (x) (if (Occurrent x) (occurrentPartOf x x))) // axiom label in BFO2 CLIF: [113-002]
b occurrent_part_of c =Def. b is a part of c & b and c are occurrents. (axiom label in BFO2 Reference: [003-002])
(forall (x y t) (if (and (occurrentPartOf x y t) (not (= x y))) (exists (z) (and (occurrentPartOf z y t) (not (exists (w) (and (occurrentPartOf w x t) (occurrentPartOf w z t)))))))) // axiom label in BFO2 CLIF: [124-001]
occurrent_part_of is antisymmetric. (axiom label in BFO2 Reference: [123-001])
occurrent_part_of is reflexive (every occurrent entity is an occurrent_part_of itself). (axiom label in BFO2 Reference: [113-002])
occurrent_part_of satisfies weak supplementation. (axiom label in BFO2 Reference: [124-001])
process profile of
profile-of
processProfileOf
proper temporal part of
t-ppart-of
properTemporalPartOf
proper part of continuant at all times
(iff (properContinuantPartOfAt a b t) (and (continuantPartOfAt a b t) (not (= a b)))) // axiom label in BFO2 CLIF: [004-001]
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'proper part of continuant at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'proper part of continuant@en(x,y,t)'.
b proper_continuant_part_of c at t =Def. b continuant_part_of c at t & b and c are not identical. (axiom label in BFO2 Reference: [004-001])
properContinuantPartOfAt
c-ppart-of_at
b proper_continuant_part_of c at t =Def. b continuant_part_of c at t & b and c are not identical. (axiom label in BFO2 Reference: [004-001])
(iff (properContinuantPartOfAt a b t) (and (continuantPartOfAt a b t) (not (= a b)))) // axiom label in BFO2 CLIF: [004-001]
proper part of occurrent
(iff (properOccurrentPartOf a b) (and (occurrentPartOf a b) (not (= a b)))) // axiom label in BFO2 CLIF: [005-001]
b proper_occurrent_part_of c =Def. b occurrent_part_of c & b and c are not identical. (axiom label in BFO2 Reference: [005-001])
o-ppart-of
properOccurrentPartOf
[copied from inverse property 'has proper occurrent part'] b has_proper_occurrent_part c = Def. c proper_occurrent_part_of b. [XXX-001
b proper_occurrent_part_of c =Def. b occurrent_part_of c & b and c are not identical. (axiom label in BFO2 Reference: [005-001])
(iff (properOccurrentPartOf a b) (and (occurrentPartOf a b) (not (= a b)))) // axiom label in BFO2 CLIF: [005-001]
temporal part of
t-part-of
(iff (temporalPartOf a b) (and (occurrentPartOf a b) (exists (t) (and (TemporalRegion t) (occupiesSpatioTemporalRegion a t))) (forall (c t_1) (if (and (Occurrent c) (occupiesSpatioTemporalRegion c t_1) (occurrentPartOf t_1 r)) (iff (occurrentPartOf c a) (occurrentPartOf c b)))))) // axiom label in BFO2 CLIF: [078-003]
(iff (properTemporalPartOf a b) (and (temporalPartOf a b) (not (= a b)))) // axiom label in BFO2 CLIF: [116-001]
temporalPartOf
(forall (x y) (if (properTemporalPartOf x y) (exists (z) (and (properTemporalPartOf z y) (not (exists (w) (and (temporalPartOf w x) (temporalPartOf w z)))))))) // axiom label in BFO2 CLIF: [117-002]
b proper_temporal_part_of c =Def. b temporal_part_of c & not (b = c). (axiom label in BFO2 Reference: [116-001])
b temporal_part_of c =Def.b occurrent_part_of c & & for some temporal region t, b occupies_temporal_region t & for all occurrents d, t (if d occupies_temporal_region t & t? occurrent_part_of t then (d occurrent_part_of a iff d occurrent_part_of b)). (axiom label in BFO2 Reference: [078-003])
if b proper_temporal_part_of c, then there is some d which is a proper_temporal_part_of c and which shares no parts with b. (axiom label in BFO2 Reference: [117-002])
the 4th year of your life is a temporal part of your life\. The first quarter of a game of football is a temporal part of the whole game\. The process of your heart beating from 4pm to 5pm today is a temporal part of the entire process of your heart beating.\ The 4th year of your life is a temporal part of your life
the process boundary which separates the 3rd and 4th years of your life.
your heart beating from 4pm to 5pm today is a temporal part of the process of your heart beating
(forall (x y) (if (properTemporalPartOf x y) (exists (z) (and (properTemporalPartOf z y) (not (exists (w) (and (temporalPartOf w x) (temporalPartOf w z)))))))) // axiom label in BFO2 CLIF: [117-002]
b temporal_part_of c =Def.b occurrent_part_of c & & for some temporal region t, b occupies_temporal_region t & for all occurrents d, t (if d occupies_temporal_region t & t? occurrent_part_of t then (d occurrent_part_of a iff d occurrent_part_of b)). (axiom label in BFO2 Reference: [078-003])
b proper_temporal_part_of c =Def. b temporal_part_of c & not (b = c). (axiom label in BFO2 Reference: [116-001])
(iff (properTemporalPartOf a b) (and (temporalPartOf a b) (not (= a b)))) // axiom label in BFO2 CLIF: [116-001]
if b proper_temporal_part_of c, then there is some d which is a proper_temporal_part_of c and which shares no parts with b. (axiom label in BFO2 Reference: [117-002])
(iff (temporalPartOf a b) (and (occurrentPartOf a b) (exists (t) (and (TemporalRegion t) (occupiesSpatioTemporalRegion a t))) (forall (c t_1) (if (and (Occurrent c) (occupiesSpatioTemporalRegion c t_1) (occurrentPartOf t_1 r)) (iff (occurrentPartOf c a) (occurrentPartOf c b)))))) // axiom label in BFO2 CLIF: [078-003]
projects onto spatial region at some time
st-projects-onto-s_st
spatial projection of spatiotemporal at some time
s-projection-of-st_st
projects onto temporal region
st-projects-onto-t
temporal projection of spatiotemporal
t-projection-of-st
occupies temporal region
occupiesTemporalRegion
spans
p occupies_temporal_region t. This is a primitive relation between an occurrent p and the temporal region t upon which the spatiotemporal region p occupies_spatiotemporal_region projects. (axiom label in BFO2 Reference: [132-001])
p occupies_temporal_region t. This is a primitive relation between an occurrent p and the temporal region t upon which the spatiotemporal region p occupies_spatiotemporal_region projects. (axiom label in BFO2 Reference: [132-001])
has temporal occupant
[copied from inverse property 'occupies temporal region'] p occupies_temporal_region t. This is a primitive relation between an occurrent p and the temporal region t upon which the spatiotemporal region p occupies_spatiotemporal_region projects. (axiom label in BFO2 Reference: [132-001])
spanOf
span-of
during which exists
during-which-exists
[copied from inverse property 'exists at'] b exists_at t means: b is an entity which exists at some temporal region t. (axiom label in BFO2 Reference: [118-002])
[copied from inverse property 'exists at'] BFO2 Reference: entity
[copied from inverse property 'exists at'] BFO2 Reference: temporal region
bearer of at all times
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'bearer of at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'bearer of@en(x,y,t)'.
BFO2 Reference: independent continuant that is not a spatial region
BFO2 Reference: specifically dependent continuant
(iff (bearerOfAt a b t) (and (specificallyDependsOnAt b a t) (IndependentContinuant a) (not (SpatialRegion a)) (existsAt b t))) // axiom label in BFO2 CLIF: [053-004]
b bearer_of c at t =Def. c s-depends_on b at t & b is an independent continuant that is not a spatial region. (axiom label in BFO2 Reference: [053-004])
bearer-of_at
bearerOfAt
(iff (bearerOfAt a b t) (and (specificallyDependsOnAt b a t) (IndependentContinuant a) (not (SpatialRegion a)) (existsAt b t))) // axiom label in BFO2 CLIF: [053-004]
b bearer_of c at t =Def. c s-depends_on b at t & b is an independent continuant that is not a spatial region. (axiom label in BFO2 Reference: [053-004])
has quality at all times
has-q_at
has function at all times
has-f_at
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'has function at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'has function@en(x,y,t)'.
(iff (hasFunctionAt a b t) (functionOf b a t)) // axiom label in BFO2 CLIF: [070-001]
a has_function b at t =Def. b function_of a at t. (axiom label in BFO2 Reference: [070-001])
hasFunctionAt
a has_function b at t =Def. b function_of a at t. (axiom label in BFO2 Reference: [070-001])
(iff (hasFunctionAt a b t) (functionOf b a t)) // axiom label in BFO2 CLIF: [070-001]
has role at all times
hasRoleAt
has-r_at
(iff (hasRoleAt a b t) (roleOfAt b a t)) // axiom label in BFO2 CLIF: [068-001]
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'has role at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'has role@en(x,y,t)'.
a has_role b at t =Def. b role_of a at t. (axiom label in BFO2 Reference: [068-001])
(iff (hasRoleAt a b t) (roleOfAt b a t)) // axiom label in BFO2 CLIF: [068-001]
a has_role b at t =Def. b role_of a at t. (axiom label in BFO2 Reference: [068-001])
has disposition at all times
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'has disposition at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'has disposition@en(x,y,t)'.
a has_disposition b at t =Def. b disposition_of a at t. (axiom label in BFO2 Reference: [069-001])
has-d_at
hasDispositionAt
(iff (hasDispositionAt a b t) (dispositionOf b a t)) // axiom label in BFO2 CLIF: [069-001]
a has_disposition b at t =Def. b disposition_of a at t. (axiom label in BFO2 Reference: [069-001])
(iff (hasDispositionAt a b t) (dispositionOf b a t)) // axiom label in BFO2 CLIF: [069-001]
material basis of at all times
material-basis-of_at
concretizes at all times
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'concretizes at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'concretizes@en(x,y,t)'.
(forall (x y t) (if (concretizesAt x y t) (and (SpecificallyDependentContinuant x) (GenericallyDependentContinuant y) (exists (z) (and (IndependentContinuant z) (specificallyDependsOnAt x z t) (genericallyDependsOnAt y z t)))))) // axiom label in BFO2 CLIF: [075-002]
concretizes_at
(forall (x y t) (if (genericallyDependsOnAt x y t) (exists (z) (and (concretizesAt z x t) (specificallyDependsOnAt z y t))))) // axiom label in BFO2 CLIF: [076-001]
You may concretize a piece of software by installing it in your computer
You may concretize a recipe that you find in a cookbook by turning it into a plan which exists as a realizable dependent continuant in your head.
b concretizes c at t means: b is a specifically dependent continuant & c is a generically dependent continuant & for some independent continuant that is not a spatial region d, b s-depends_on d at t & c g-depends on d at t & if c migrates from bearer d to another bearer e than a copy of b will be created in e. (axiom label in BFO2 Reference: [075-002])
concretizesAt
if b g-depends on c at some time t, then there is some d, such that d concretizes b at t and d s-depends_on c at t. (axiom label in BFO2 Reference: [076-001])
you may concretize a poem as a pattern of memory traces in your head
(forall (x y t) (if (concretizesAt x y t) (and (SpecificallyDependentContinuant x) (GenericallyDependentContinuant y) (exists (z) (and (IndependentContinuant z) (specificallyDependsOnAt x z t) (genericallyDependsOnAt y z t)))))) // axiom label in BFO2 CLIF: [075-002]
(forall (x y t) (if (genericallyDependsOnAt x y t) (exists (z) (and (concretizesAt z x t) (specificallyDependsOnAt z y t))))) // axiom label in BFO2 CLIF: [076-001]
if b g-depends on c at some time t, then there is some d, such that d concretizes b at t and d s-depends_on c at t. (axiom label in BFO2 Reference: [076-001])
b concretizes c at t means: b is a specifically dependent continuant & c is a generically dependent continuant & for some independent continuant that is not a spatial region d, b s-depends_on d at t & c g-depends on d at t & if c migrates from bearer d to another bearer e than a copy of b will be created in e. (axiom label in BFO2 Reference: [075-002])
concretized by at all times
concretized-by_at
participates in at all times
participatesInAt
participates-in_at
has participant at all times
BFO2 Reference: independent continuant that is not a spatial region, specifically dependent continuant, generically dependent continuant
BFO2 Reference: process
(forall (x y t) (if (and (hasParticipantAt x y t) (GenericallyDependentContinuant y)) (exists (z) (and (IndependentContinuant z) (not (SpatialRegion z)) (genericallyDependsOn y z t) (specificallyDependsOnAt x z t))))) // axiom label in BFO2 CLIF: [091-003]
(forall (x y t) (if (hasParticipantAt x y t) (Occurrent x))) // axiom label in BFO2 CLIF: [087-001]
(forall (x y t) (if (and (hasParticipantAt x y t) (SpecificallyDependentContinuant y)) (exists (z) (and (IndependentContinuant z) (not (SpatialRegion z)) (specificallyDependsOnAt x z t) (specificallyDependsOnAt y z t))))) // axiom label in BFO2 CLIF: [090-003]
(forall (x y t) (if (hasParticipantAt x y t) (existsAt y t))) // axiom label in BFO2 CLIF: [089-001]
has-participant_at
(forall (x y t) (if (hasParticipantAt x y t) (Continuant y))) // axiom label in BFO2 CLIF: [088-001]
hasParticipantAt
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'has participant at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'has participant@en(x,y,t)'.
BFO 2 Reference: Spatial regions do not participate in processes.
has_participant is an instance-level relation between a process, a continuant, and a temporal region at which the continuant participates in some way in the process. (axiom label in BFO2 Reference: [086-003])
if b has_participant c at t & c is a generically dependent continuant, then there is some independent continuant that is not a spatial region d, and which is such that c g-depends on d at t & b s-depends_on d at t. (axiom label in BFO2 Reference: [091-003])
if b has_participant c at t & c is a specifically dependent continuant, then there is some independent continuant that is not a spatial region d, c s-depends_on d at t & b s-depends_on d at t. (axiom label in BFO2 Reference: [090-003])
if b has_participant c at t then b is an occurrent. (axiom label in BFO2 Reference: [087-001])
if b has_participant c at t then c exists at t. (axiom label in BFO2 Reference: [089-001])
if b has_participant c at t then c is a continuant. (axiom label in BFO2 Reference: [088-001])
has_participant is an instance-level relation between a process, a continuant, and a temporal region at which the continuant participates in some way in the process. (axiom label in BFO2 Reference: [086-003])
if b has_participant c at t & c is a generically dependent continuant, then there is some independent continuant that is not a spatial region d, and which is such that c g-depends on d at t & b s-depends_on d at t. (axiom label in BFO2 Reference: [091-003])
(forall (x y t) (if (and (hasParticipantAt x y t) (SpecificallyDependentContinuant y)) (exists (z) (and (IndependentContinuant z) (not (SpatialRegion z)) (specificallyDependsOnAt x z t) (specificallyDependsOnAt y z t))))) // axiom label in BFO2 CLIF: [090-003]
(forall (x y t) (if (hasParticipantAt x y t) (existsAt y t))) // axiom label in BFO2 CLIF: [089-001]
if b has_participant c at t then c is a continuant. (axiom label in BFO2 Reference: [088-001])
(forall (x y t) (if (hasParticipantAt x y t) (Continuant y))) // axiom label in BFO2 CLIF: [088-001]
if b has_participant c at t then b is an occurrent. (axiom label in BFO2 Reference: [087-001])
(forall (x y t) (if (hasParticipantAt x y t) (Occurrent x))) // axiom label in BFO2 CLIF: [087-001]
(forall (x y t) (if (and (hasParticipantAt x y t) (GenericallyDependentContinuant y)) (exists (z) (and (IndependentContinuant z) (not (SpatialRegion z)) (genericallyDependsOn y z t) (specificallyDependsOnAt x z t))))) // axiom label in BFO2 CLIF: [091-003]
if b has_participant c at t then c exists at t. (axiom label in BFO2 Reference: [089-001])
if b has_participant c at t & c is a specifically dependent continuant, then there is some independent continuant that is not a spatial region d, c s-depends_on d at t & b s-depends_on d at t. (axiom label in BFO2 Reference: [090-003])
has specific dependent at all times
has-s-dep_at
specifically depends on at some time
s-depends-on_st
(forall (x y t) (if (and (Occurrent x) (IndependentContinuant y) (specificallyDependsOnAt x y t)) (forall (t_1) (if (existsAt x t_1) (specificallyDependsOnAt x y t_1))))) // axiom label in BFO2 CLIF: [015-002]
BFO2 Reference: specifically dependent continuant\; process; process boundary
(forall (x y t) (if (specificallyDependsOnAt x y t) (exists (z) (and (IndependentContinuant z) (not (SpatialRegion z)) (specificallyDependsOnAt x z t))))) // axiom label in BFO2 CLIF: [136-001]
specificallyDependsOn
(forall (x y z t) (if (and (specificallyDependsOnAt x y t) (specificallyDependsOnAt y z t)) (specificallyDependsOnAt x z t))) // axiom label in BFO2 CLIF: [054-002]
(forall (x) (if (exists (y t) (specificallyDependsOnAt x y t)) (not (MaterialEntity x)))) // axiom label in BFO2 CLIF: [052-001]
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'specifically depends on at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'specifically depends on@en'(x,y,t)
(forall (x y t) (if (and (Entity x) (or (continuantPartOfAt y x t) (continuantPartOfAt x y t) (occurrentPartOf x y) (occurrentPartOf y x))) (not (specificallyDependsOnAt x y t)))) // axiom label in BFO2 CLIF: [013-002]
A pain s-depends_on the organism that is experiencing the pain
BFO 2 Reference: An entity – for example an act of communication or a game of football – can s-depends_on more than one entity. Complex phenomena for example in the psychological and social realms (such as inferring, commanding and requesting) or in the realm of multi-organismal biological processes (such as infection and resistance), will involve multiple families of dependence relations, involving both continuants and occurrents [1, 4, 28
BFO 2 Reference: S-dependence is just one type of dependence among many; it is what, in the literature, is referred to as ‘existential dependence’ [87, 46, 65, 20
BFO 2 Reference: the relation of s-depends_on does not in every case require simultaneous existence of its relata. Note the difference between such cases and the cases of continuant universals defined historically: the act of answering depends existentially on the prior act of questioning; the human being who was baptized or who answered a question does not himself depend existentially on the prior act of baptism or answering. He would still exist even if these acts had never taken place.
If b is s-depends_on something at some time, then b is not a material entity. (axiom label in BFO2 Reference: [052-001])
If b s-depends_on something at t, then there is some c, which is an independent continuant and not a spatial region, such that b s-depends_on c at t. (axiom label in BFO2 Reference: [136-001])
If occurrent b s-depends_on some independent continuant c at t, then b s-depends_on c at every time at which b exists. (axiom label in BFO2 Reference: [015-002])
To say that b s-depends_on a at t is to say that b and c do not share common parts & b is of its nature such that it cannot exist unless c exists & b is not a boundary of c and b is not a site of which c is the host [64
a gait s-depends_on the walking object. (All at some specific time.)
a shape s-depends_on the shaped object
an entity does not s-depend_on any of its (continuant or occurrent) parts or on anything it is part of. (axiom label in BFO2 Reference: [013-002])
if b s-depends_on c at t & c s-depends_on d at t then b s-depends_on d at t. (axiom label in BFO2 Reference: [054-002])
one-sided s-dependence of a dependent continuant on an independent continuant: an instance of headache s-depends_on some head
one-sided s-dependence of a dependent continuant on an independent continuant: an instance of temperature s-depends_on some organism
one-sided s-dependence of a process on something: a process of cell death s-depends_on a cell
one-sided s-dependence of a process on something: an instance of seeing (a relational process) s-depends_on some organism and on some seen entity, which may be an occurrent or a continuant
one-sided s-dependence of one occurrent on another: a process of answering a question is dependent on a prior process of asking a question
one-sided s-dependence of one occurrent on another: a process of obeying a command is dependent on a prior process of issuing a command
one-sided s-dependence of one occurrent on multiple independent continuants: a relational process of hitting a ball with a cricket bat
one-sided s-dependence of one occurrent on multiple independent continuants: a relational process of paying cash to a merchant in exchange for a bag of figs
reciprocal s-dependence between occurrents: a process of buying and the associated process of selling
reciprocal s-dependence between occurrents: a process of increasing the volume of a portion of gas while temperature remains constant and the associated process of decreasing the pressure exerted by the gas
reciprocal s-dependence between occurrents: in a game of chess the process of playing with the white pieces is mutually dependent on the process of playing with the black pieces
the one-sided dependence of an occurrent on an independent continuant: football match on the players, the ground, the ball
the one-sided dependence of an occurrent on an independent continuant: handwave on a hand
the three-sided reciprocal s-dependence of the hue, saturation and brightness of a color [45
the three-sided reciprocal s-dependence of the pitch, timbre and volume of a tone [45
the two-sided reciprocal s-dependence of the roles of husband and wife [20
an entity does not s-depend_on any of its (continuant or occurrent) parts or on anything it is part of. (axiom label in BFO2 Reference: [013-002])
(forall (x) (if (exists (y t) (specificallyDependsOnAt x y t)) (not (MaterialEntity x)))) // axiom label in BFO2 CLIF: [052-001]
(forall (x y t) (if (and (Occurrent x) (IndependentContinuant y) (specificallyDependsOnAt x y t)) (forall (t_1) (if (existsAt x t_1) (specificallyDependsOnAt x y t_1))))) // axiom label in BFO2 CLIF: [015-002]
If b is s-depends_on something at some time, then b is not a material entity. (axiom label in BFO2 Reference: [052-001])
if b s-depends_on c at t & c s-depends_on d at t then b s-depends_on d at t. (axiom label in BFO2 Reference: [054-002])
(forall (x y t) (if (and (Entity x) (or (continuantPartOfAt y x t) (continuantPartOfAt x y t) (occurrentPartOf x y) (occurrentPartOf y x))) (not (specificallyDependsOnAt x y t)))) // axiom label in BFO2 CLIF: [013-002]
(forall (x y t) (if (specificallyDependsOnAt x y t) (exists (z) (and (IndependentContinuant z) (not (SpatialRegion z)) (specificallyDependsOnAt x z t))))) // axiom label in BFO2 CLIF: [136-001]
(forall (x y z t) (if (and (specificallyDependsOnAt x y t) (specificallyDependsOnAt y z t)) (specificallyDependsOnAt x z t))) // axiom label in BFO2 CLIF: [054-002]
If b s-depends_on something at t, then there is some c, which is an independent continuant and not a spatial region, such that b s-depends_on c at t. (axiom label in BFO2 Reference: [136-001])
If occurrent b s-depends_on some independent continuant c at t, then b s-depends_on c at every time at which b exists. (axiom label in BFO2 Reference: [015-002])
has location at all times
has-location_at
located in at some time
(forall (x y z t) (if (and (IndependentContinuant x) (IndependentContinuant y) (IndependentContinuant z) (locatedInAt x y t) (continuantPartOfAt y z t)) (locatedInAt x z t))) // axiom label in BFO2 CLIF: [049-001]
BFO2 Reference: independent continuant
(forall (x y z t) (if (and (locatedInAt x y t) (locatedInAt y z t)) (locatedInAt x z t))) // axiom label in BFO2 CLIF: [046-001]
(iff (locatedInAt a b t) (and (IndependentContinuant a) (IndependentContinuant b) (exists (r_1 r_2) (and (occupiesSpatialRegionAt a r_1 t) (occupiesSpatialRegionAt b r_2 t) (continuantPartOfAt r_1 r_2 t))))) // axiom label in BFO2 CLIF: [045-001]
locatedInAt
located-in_st
(forall (x y z t) (if (and (IndependentContinuant x) (IndependentContinuant y) (IndependentContinuant z) (continuantPartOfAt x y t) (locatedInAt y z t)) (locatedInAt x z t))) // axiom label in BFO2 CLIF: [048-001]
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'located in at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'located in@en'(x,y,t)
Located_in is transitive. (axiom label in BFO2 Reference: [046-001])
Mary located_in Salzburg
b located_in c at t = Def. b and c are independent continuants, and the region at which b is located at t is a (proper or improper) continuant_part_of the region at which c is located at t. (axiom label in BFO2 Reference: [045-001])
for all independent continuants b, c, and d: if b continuant_part_of c at t & c located_in d at t, then b located_in d at t. (axiom label in BFO2 Reference: [048-001])
for all independent continuants b, c, and d: if b located_in c at t & c continuant_part_of d at t, then b located_in d at t. (axiom label in BFO2 Reference: [049-001])
the Empire State Building located_in New York.
this portion of cocaine located_in this portion of blood
this stem cell located_in this portion of bone marrow
your arm located_in your body
Located_in is transitive. (axiom label in BFO2 Reference: [046-001])
(forall (x y z t) (if (and (IndependentContinuant x) (IndependentContinuant y) (IndependentContinuant z) (continuantPartOfAt x y t) (locatedInAt y z t)) (locatedInAt x z t))) // axiom label in BFO2 CLIF: [048-001]
b located_in c at t = Def. b and c are independent continuants, and the region at which b is located at t is a (proper or improper) continuant_part_of the region at which c is located at t. (axiom label in BFO2 Reference: [045-001])
(iff (locatedInAt a b t) (and (IndependentContinuant a) (IndependentContinuant b) (exists (r_1 r_2) (and (occupiesSpatialRegionAt a r_1 t) (occupiesSpatialRegionAt b r_2 t) (continuantPartOfAt r_1 r_2 t))))) // axiom label in BFO2 CLIF: [045-001]
for all independent continuants b, c, and d: if b located_in c at t & c continuant_part_of d at t, then b located_in d at t. (axiom label in BFO2 Reference: [049-001])
(forall (x y z t) (if (and (locatedInAt x y t) (locatedInAt y z t)) (locatedInAt x z t))) // axiom label in BFO2 CLIF: [046-001]
for all independent continuants b, c, and d: if b continuant_part_of c at t & c located_in d at t, then b located_in d at t. (axiom label in BFO2 Reference: [048-001])
(forall (x y z t) (if (and (IndependentContinuant x) (IndependentContinuant y) (IndependentContinuant z) (locatedInAt x y t) (continuantPartOfAt y z t)) (locatedInAt x z t))) // axiom label in BFO2 CLIF: [049-001]
has member part at all times
has-member-part_at
member part of at all times
BFO2 Reference: object
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'member part of at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'member part of@en(x,y,t)'.
memberPartOfAt
BFO2 Reference: object aggregate
member-part-of_at
(forall (x y t) (if (memberPartOfAt x y t) (continuantPartOfAt x y t))) // axiom label in BFO2 CLIF: [104-001]
b member_part_of c at t =Def. b is an object & there is at t a mutually exhaustive and pairwise disjoint partition of c into objects x1, …, xn (for some n > 1) with b = xi for some 1 ? i ? n. (axiom label in BFO2 Reference: [026-004])
each piece in a chess set is a member part of the chess set; each Beatle in the collection called The Beatles is a member part of The Beatles.
each tree in a forest is a member_part of the forest
if b member_part_of c at t then b continuant_part_of c at t. (axiom label in BFO2 Reference: [104-001])
b member_part_of c at t =Def. b is an object & there is at t a mutually exhaustive and pairwise disjoint partition of c into objects x1, …, xn (for some n > 1) with b = xi for some 1 ? i ? n. (axiom label in BFO2 Reference: [026-004])
if b member_part_of c at t then b continuant_part_of c at t. (axiom label in BFO2 Reference: [104-001])
(forall (x y t) (if (memberPartOfAt x y t) (continuantPartOfAt x y t))) // axiom label in BFO2 CLIF: [104-001]
has proper continuant part at some time
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'has proper continuant part at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'has proper continuant part@en'(x,y,t)
b has_proper_continuant_part c at t = Def. c proper_continuant_part_of b at t. [XXX-001
c-has-ppart_st
[copied from inverse property 'proper part of continuant at some time'] b proper_continuant_part_of c at t =Def. b continuant_part_of c at t & b and c are not identical. (axiom label in BFO2 Reference: [004-001])
hasProperContinuantPartAt
[copied from inverse property 'proper part of continuant at some time'] Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'proper part of continuant at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'proper part of continuant@en'(x,y,t)
proper part of continuant at some time
c-ppart-of_st
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'proper part of continuant at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'proper part of continuant@en'(x,y,t)
properContinuantPartOfAt
[copied from inverse property 'has proper continuant part at some time'] b has_proper_continuant_part c at t = Def. c proper_continuant_part_of b at t. [XXX-001
[copied from inverse property 'has proper continuant part at some time'] Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'has proper continuant part at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'has proper continuant part@en'(x,y,t)
(iff (properContinuantPartOfAt a b t) (and (continuantPartOfAt a b t) (not (= a b)))) // axiom label in BFO2 CLIF: [004-001]
b proper_continuant_part_of c at t =Def. b continuant_part_of c at t & b and c are not identical. (axiom label in BFO2 Reference: [004-001])
b proper_continuant_part_of c at t =Def. b continuant_part_of c at t & b and c are not identical. (axiom label in BFO2 Reference: [004-001])
(iff (properContinuantPartOfAt a b t) (and (continuantPartOfAt a b t) (not (= a b)))) // axiom label in BFO2 CLIF: [004-001]
part of continuant at some time
(forall (x y t) (if (and (continuantPartOfAt x y t) (not (= x y))) (exists (z) (and (continuantPartOfAt z y t) (not (exists (w) (and (continuantPartOfAt w x t) (continuantPartOfAt w z t)))))))) // axiom label in BFO2 CLIF: [121-001]
(forall (x y z t) (if (and (continuantPartOfAt x y t) (continuantPartOfAt y z t)) (continuantPartOfAt x z t))) // axiom label in BFO2 CLIF: [110-001]
continuantPartOfAt
(forall (x y t) (if (and (continuantPartOfAt x y t) (continuantPartOfAt y x t)) (= x y))) // axiom label in BFO2 CLIF: [120-001]
BFO2 Reference: continuantThe range for ‘t’ (as in all cases throughout this document unless otherwise specified) is: temporal region.
(forall (x y t) (if (and (continuantPartOfAt x y t) (IndependentContinuant x)) (locatedInAt x y t))) // axiom label in BFO2 CLIF: [047-002]
BFO2 Reference: continuant
(forall (x y t) (if (exists (v) (and (continuantPartOfAt v x t) (continuantPartOfAt v y t))) (exists (z) (forall (u w) (iff (iff (continuantPartOfAt w u t) (and (continuantPartOfAt w x t) (continuantPartOfAt w y t))) (= z u)))))) // axiom label in BFO2 CLIF: [122-001]
[copied from inverse property 'has continuant part at some time'] Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'has continuant part at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'has continuant part@en'(x,y,t)
(forall (x t) (if (Continuant x) (continuantPartOfAt x x t))) // axiom label in BFO2 CLIF: [111-002]
(iff (ImmaterialEntity a) (and (IndependentContinuant a) (not (exists (b t) (and (MaterialEntity b) (continuantPartOfAt b a t)))))) // axiom label in BFO2 CLIF: [028-001]
[copied from inverse property 'has continuant part at some time'] b has_continuant_part c at t = Def. c continuant_part_of b at t. (axiom label in BFO2 Reference: [006-001])
c-part-of_st
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'part of continuant at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'part of continuant@en'(x,y,t)
BFO 2 Reference: Immaterial entities are in some cases continuant parts of their material hosts. Thus the hold of a ship, for example, is a part of the ship; it may itself have parts, which may have names (used for example by ship stow planners, customs inspectors, and the like). Immaterial entities under both 1. and 2. can be of zero, one, two or three dimensions. We define:a(immaterial entity)[Definition: a is an immaterial entity = Def. a is an independent continuant that has no material entities as parts. (axiom label in BFO2 Reference: [028-001])
BFO 2 Reference: a (continuant or occurrent) part of itself. We appreciate that this is counterintuitive for some users, since it implies for example that President Obama is a part of himself. However it brings benefits in simplifying the logical formalism, and it captures an important feature of identity, namely that it is the limit case of mereological inclusion.
Mary’s arm continuant_part_of Mary in the time of her life prior to her operation
b continuant_part_of c at t =Def. b is a part of c at t & t is a time & b and c are continuants. (axiom label in BFO2 Reference: [002-001])
continuant_part_of is antisymmetric. (axiom label in BFO2 Reference: [120-001])
continuant_part_of is reflexive (every continuant entity is a continuant_part_of itself). (axiom label in BFO2 Reference: [111-002])
continuant_part_of is transitive. (axiom label in BFO2 Reference: [110-001])
continuant_part_of satisfies unique product. (axiom label in BFO2 Reference: [122-001])
continuant_part_of satisfies weak supplementation. (axiom label in BFO2 Reference: [121-001])
if b continuant_part_of c at t and b is an independent continuant, then b is located_in c at t. (axiom label in BFO2 Reference: [047-002])
the Northern hemisphere of the planet Earth is a part of the planet Earth at all times at which the planet Earth exists.
continuant_part_of satisfies weak supplementation. (axiom label in BFO2 Reference: [121-001])
continuant_part_of satisfies unique product. (axiom label in BFO2 Reference: [122-001])
continuant_part_of is transitive. (axiom label in BFO2 Reference: [110-001])
(forall (x t) (if (Continuant x) (continuantPartOfAt x x t))) // axiom label in BFO2 CLIF: [111-002]
(forall (x y z t) (if (and (continuantPartOfAt x y t) (continuantPartOfAt y z t)) (continuantPartOfAt x z t))) // axiom label in BFO2 CLIF: [110-001]
(forall (x y t) (if (and (continuantPartOfAt x y t) (continuantPartOfAt y x t)) (= x y))) // axiom label in BFO2 CLIF: [120-001]
BFO 2 Reference: Immaterial entities are in some cases continuant parts of their material hosts. Thus the hold of a ship, for example, is a part of the ship; it may itself have parts, which may have names (used for example by ship stow planners, customs inspectors, and the like). Immaterial entities under both 1. and 2. can be of zero, one, two or three dimensions. We define:a(immaterial entity)[Definition: a is an immaterial entity = Def. a is an independent continuant that has no material entities as parts. (axiom label in BFO2 Reference: [028-001])
(forall (x y t) (if (and (continuantPartOfAt x y t) (not (= x y))) (exists (z) (and (continuantPartOfAt z y t) (not (exists (w) (and (continuantPartOfAt w x t) (continuantPartOfAt w z t)))))))) // axiom label in BFO2 CLIF: [121-001]
(forall (x y t) (if (and (continuantPartOfAt x y t) (IndependentContinuant x)) (locatedInAt x y t))) // axiom label in BFO2 CLIF: [047-002]
if b continuant_part_of c at t and b is an independent continuant, then b is located_in c at t. (axiom label in BFO2 Reference: [047-002])
(iff (ImmaterialEntity a) (and (IndependentContinuant a) (not (exists (b t) (and (MaterialEntity b) (continuantPartOfAt b a t)))))) // axiom label in BFO2 CLIF: [028-001]
continuant_part_of is reflexive (every continuant entity is a continuant_part_of itself). (axiom label in BFO2 Reference: [111-002])
b continuant_part_of c at t =Def. b is a part of c at t & t is a time & b and c are continuants. (axiom label in BFO2 Reference: [002-001])
(forall (x y t) (if (exists (v) (and (continuantPartOfAt v x t) (continuantPartOfAt v y t))) (exists (z) (forall (u w) (iff (iff (continuantPartOfAt w u t) (and (continuantPartOfAt w x t) (continuantPartOfAt w y t))) (= z u)))))) // axiom label in BFO2 CLIF: [122-001]
continuant_part_of is antisymmetric. (axiom label in BFO2 Reference: [120-001])
part of continuant at all times
(forall (x y t) (if (and (continuantPartOfAt x y t) (IndependentContinuant x)) (locatedInAt x y t))) // axiom label in BFO2 CLIF: [047-002]
(forall (x y t) (if (and (continuantPartOfAt x y t) (not (= x y))) (exists (z) (and (continuantPartOfAt z y t) (not (exists (w) (and (continuantPartOfAt w x t) (continuantPartOfAt w z t)))))))) // axiom label in BFO2 CLIF: [121-001]
BFO2 Reference: continuant
continuantPartOfAt
c-part-of_at
[copied from inverse property 'has continuant part at all times that part exists'] This is a binary version of a ternary time-indexed, instance level, relation. Unlike the rest of the temporalized relations which temporally quantify over existence of the subject of the relation, this relation temporally quantifies over the existence of the object of the relation. The relation is provided tentatively, to assess whether the GO needs such a relation. It is inverse of 'part of continuant at all times'
(forall (x y z t) (if (and (continuantPartOfAt x y t) (continuantPartOfAt y z t)) (continuantPartOfAt x z t))) // axiom label in BFO2 CLIF: [110-001]
(forall (x y t) (if (and (continuantPartOfAt x y t) (continuantPartOfAt y x t)) (= x y))) // axiom label in BFO2 CLIF: [120-001]
[copied from inverse property 'has continuant part at all times that part exists'] forall(t) exists_at(y,t) -> exists_at(x,t) and 'has continuant part'(x,y,t)
BFO2 Reference: continuantThe range for ‘t’ (as in all cases throughout this document unless otherwise specified) is: temporal region.
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'part of continuant at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'part of continuant@en(x,y,t)'.
(forall (x y t) (if (exists (v) (and (continuantPartOfAt v x t) (continuantPartOfAt v y t))) (exists (z) (forall (u w) (iff (iff (continuantPartOfAt w u t) (and (continuantPartOfAt w x t) (continuantPartOfAt w y t))) (= z u)))))) // axiom label in BFO2 CLIF: [122-001]
(forall (x t) (if (Continuant x) (continuantPartOfAt x x t))) // axiom label in BFO2 CLIF: [111-002]
(iff (ImmaterialEntity a) (and (IndependentContinuant a) (not (exists (b t) (and (MaterialEntity b) (continuantPartOfAt b a t)))))) // axiom label in BFO2 CLIF: [028-001]
BFO 2 Reference: Immaterial entities are in some cases continuant parts of their material hosts. Thus the hold of a ship, for example, is a part of the ship; it may itself have parts, which may have names (used for example by ship stow planners, customs inspectors, and the like). Immaterial entities under both 1. and 2. can be of zero, one, two or three dimensions. We define:a(immaterial entity)[Definition: a is an immaterial entity = Def. a is an independent continuant that has no material entities as parts. (axiom label in BFO2 Reference: [028-001])
BFO 2 Reference: a (continuant or occurrent) part of itself. We appreciate that this is counterintuitive for some users, since it implies for example that President Obama is a part of himself. However it brings benefits in simplifying the logical formalism, and it captures an important feature of identity, namely that it is the limit case of mereological inclusion.
Mary’s arm continuant_part_of Mary in the time of her life prior to her operation
b continuant_part_of c at t =Def. b is a part of c at t & t is a time & b and c are continuants. (axiom label in BFO2 Reference: [002-001])
continuant_part_of is antisymmetric. (axiom label in BFO2 Reference: [120-001])
continuant_part_of is reflexive (every continuant entity is a continuant_part_of itself). (axiom label in BFO2 Reference: [111-002])
continuant_part_of is transitive. (axiom label in BFO2 Reference: [110-001])
continuant_part_of satisfies unique product. (axiom label in BFO2 Reference: [122-001])
continuant_part_of satisfies weak supplementation. (axiom label in BFO2 Reference: [121-001])
if b continuant_part_of c at t and b is an independent continuant, then b is located_in c at t. (axiom label in BFO2 Reference: [047-002])
the Northern hemisphere of the planet Earth is a part of the planet Earth at all times at which the planet Earth exists.
(forall (x y z t) (if (and (continuantPartOfAt x y t) (continuantPartOfAt y z t)) (continuantPartOfAt x z t))) // axiom label in BFO2 CLIF: [110-001]
continuant_part_of is transitive. (axiom label in BFO2 Reference: [110-001])
b continuant_part_of c at t =Def. b is a part of c at t & t is a time & b and c are continuants. (axiom label in BFO2 Reference: [002-001])
(forall (x y t) (if (and (continuantPartOfAt x y t) (IndependentContinuant x)) (locatedInAt x y t))) // axiom label in BFO2 CLIF: [047-002]
continuant_part_of satisfies unique product. (axiom label in BFO2 Reference: [122-001])
(forall (x y t) (if (and (continuantPartOfAt x y t) (not (= x y))) (exists (z) (and (continuantPartOfAt z y t) (not (exists (w) (and (continuantPartOfAt w x t) (continuantPartOfAt w z t)))))))) // axiom label in BFO2 CLIF: [121-001]
BFO 2 Reference: Immaterial entities are in some cases continuant parts of their material hosts. Thus the hold of a ship, for example, is a part of the ship; it may itself have parts, which may have names (used for example by ship stow planners, customs inspectors, and the like). Immaterial entities under both 1. and 2. can be of zero, one, two or three dimensions. We define:a(immaterial entity)[Definition: a is an immaterial entity = Def. a is an independent continuant that has no material entities as parts. (axiom label in BFO2 Reference: [028-001])
(iff (ImmaterialEntity a) (and (IndependentContinuant a) (not (exists (b t) (and (MaterialEntity b) (continuantPartOfAt b a t)))))) // axiom label in BFO2 CLIF: [028-001]
(forall (x y t) (if (and (continuantPartOfAt x y t) (continuantPartOfAt y x t)) (= x y))) // axiom label in BFO2 CLIF: [120-001]
(forall (x t) (if (Continuant x) (continuantPartOfAt x x t))) // axiom label in BFO2 CLIF: [111-002]
continuant_part_of is antisymmetric. (axiom label in BFO2 Reference: [120-001])
(forall (x y t) (if (exists (v) (and (continuantPartOfAt v x t) (continuantPartOfAt v y t))) (exists (z) (forall (u w) (iff (iff (continuantPartOfAt w u t) (and (continuantPartOfAt w x t) (continuantPartOfAt w y t))) (= z u)))))) // axiom label in BFO2 CLIF: [122-001]
continuant_part_of satisfies weak supplementation. (axiom label in BFO2 Reference: [121-001])
if b continuant_part_of c at t and b is an independent continuant, then b is located_in c at t. (axiom label in BFO2 Reference: [047-002])
continuant_part_of is reflexive (every continuant entity is a continuant_part_of itself). (axiom label in BFO2 Reference: [111-002])
has continuant part at some time
c-has-part_st
[copied from inverse property 'part of continuant at some time'] BFO2 Reference: continuant
[copied from inverse property 'part of continuant at some time'] the Northern hemisphere of the planet Earth is a part of the planet Earth at all times at which the planet Earth exists.
[copied from inverse property 'part of continuant at some time'] b continuant_part_of c at t =Def. b is a part of c at t & t is a time & b and c are continuants. (axiom label in BFO2 Reference: [002-001])
hasContinuantPartAt
[copied from inverse property 'part of continuant at some time'] Mary’s arm continuant_part_of Mary in the time of her life prior to her operation
[copied from inverse property 'part of continuant at some time'] BFO 2 Reference: a (continuant or occurrent) part of itself. We appreciate that this is counterintuitive for some users, since it implies for example that President Obama is a part of himself. However it brings benefits in simplifying the logical formalism, and it captures an important feature of identity, namely that it is the limit case of mereological inclusion.
Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'has continuant part at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'has continuant part@en'(x,y,t)
[copied from inverse property 'part of continuant at some time'] BFO 2 Reference: Immaterial entities are in some cases continuant parts of their material hosts. Thus the hold of a ship, for example, is a part of the ship; it may itself have parts, which may have names (used for example by ship stow planners, customs inspectors, and the like). Immaterial entities under both 1. and 2. can be of zero, one, two or three dimensions. We define:a(immaterial entity)[Definition: a is an immaterial entity = Def. a is an independent continuant that has no material entities as parts. (axiom label in BFO2 Reference: [028-001])
[copied from inverse property 'part of continuant at some time'] BFO2 Reference: continuantThe range for ‘t’ (as in all cases throughout this document unless otherwise specified) is: temporal region.
(iff (hasContinuantPartAt a b t) (continuantPartOfAt b a t)) // axiom label in BFO2 CLIF: [006-001]
[copied from inverse property 'part of continuant at some time'] Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance level, relation. The BFO reading of the binary relation 'part of continuant at some time@en' is: exists t, exists_at(x,t) & exists_at(y,t) & 'part of continuant@en'(x,y,t)
b has_continuant_part c at t = Def. c continuant_part_of b at t. (axiom label in BFO2 Reference: [006-001])
(iff (hasContinuantPartAt a b t) (continuantPartOfAt b a t)) // axiom label in BFO2 CLIF: [006-001]
b has_continuant_part c at t = Def. c continuant_part_of b at t. (axiom label in BFO2 Reference: [006-001])
has proper temporal part
has-t-ppart
history of
[copied from inverse property 'has history'] b has_history c iff c history_of b [XXX-001
b history_of c if c is a material entity or site and b is a history that is the unique history of cAxiom: if b history_of c and b history_of d then c=d [XXX-001
historyOf
history-of
has history
[copied from inverse property 'history of'] b history_of c if c is a material entity or site and b is a history that is the unique history of cAxiom: if b history_of c and b history_of d then c=d [XXX-001
hasHistory
has-history
b has_history c iff c history_of b [XXX-001
part of continuant at all times that whole exists
This is a binary version of a ternary time-indexed, instance level, relation. Unlike the rest of the temporalized relations which temporally quantify over existence of the subject of the relation, this relation temporally quantifies over the existence of the object of the relation. The relation is provided tentatively, to assess whether the GO needs such a relation. It is inverse of 'has continuant part at all times'
[copied from inverse property 'has continuant part at all times'] b has_continuant_part c at t = Def. c continuant_part_of b at t. (axiom label in BFO2 Reference: [006-001])
forall(t) exists_at(y,t) -> exists_at(x,t) and 'part of continuant'(x,y,t)
[copied from inverse property 'has continuant part at all times'] Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'has continuant part at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'has continuant part@en(x,y,t)'.
c-part-of-object_at
forall(t) exists_at(y,t) -> exists_at(x,t) and 'part of continuant'(x,y,t)
This is a binary version of a ternary time-indexed, instance level, relation. Unlike the rest of the temporalized relations which temporally quantify over existence of the subject of the relation, this relation temporally quantifies over the existence of the object of the relation. The relation is provided tentatively, to assess whether the GO needs such a relation. It is inverse of 'has continuant part at all times'
has continuant part at all times that part exists
[copied from inverse property 'part of continuant at all times'] BFO2 Reference: continuantThe range for ‘t’ (as in all cases throughout this document unless otherwise specified) is: temporal region.
[copied from inverse property 'part of continuant at all times'] BFO2 Reference: continuant
[copied from inverse property 'part of continuant at all times'] BFO 2 Reference: Immaterial entities are in some cases continuant parts of their material hosts. Thus the hold of a ship, for example, is a part of the ship; it may itself have parts, which may have names (used for example by ship stow planners, customs inspectors, and the like). Immaterial entities under both 1. and 2. can be of zero, one, two or three dimensions. We define:a(immaterial entity)[Definition: a is an immaterial entity = Def. a is an independent continuant that has no material entities as parts. (axiom label in BFO2 Reference: [028-001])
[copied from inverse property 'part of continuant at all times'] BFO 2 Reference: a (continuant or occurrent) part of itself. We appreciate that this is counterintuitive for some users, since it implies for example that President Obama is a part of himself. However it brings benefits in simplifying the logical formalism, and it captures an important feature of identity, namely that it is the limit case of mereological inclusion.
[copied from inverse property 'part of continuant at all times'] b continuant_part_of c at t =Def. b is a part of c at t & t is a time & b and c are continuants. (axiom label in BFO2 Reference: [002-001])
[copied from inverse property 'part of continuant at all times'] Mary’s arm continuant_part_of Mary in the time of her life prior to her operation
This is a binary version of a ternary time-indexed, instance level, relation. Unlike the rest of the temporalized relations which temporally quantify over existence of the subject of the relation, this relation temporally quantifies over the existence of the object of the relation. The relation is provided tentatively, to assess whether the GO needs such a relation. It is inverse of 'part of continuant at all times'
c-has-part-object_at
[copied from inverse property 'part of continuant at all times'] Alan Ruttenberg: This is a binary version of a ternary time-indexed, instance-level, relation. The BFO reading of the binary relation 'part of continuant at all times@en' is: forall(t) exists_at(x,t) -> exists_at(y,t) and 'part of continuant@en(x,y,t)'.
[copied from inverse property 'part of continuant at all times'] the Northern hemisphere of the planet Earth is a part of the planet Earth at all times at which the planet Earth exists.
forall(t) exists_at(y,t) -> exists_at(x,t) and 'has continuant part'(x,y,t)
This is a binary version of a ternary time-indexed, instance level, relation. Unlike the rest of the temporalized relations which temporally quantify over existence of the subject of the relation, this relation temporally quantifies over the existence of the object of the relation. The relation is provided tentatively, to assess whether the GO needs such a relation. It is inverse of 'part of continuant at all times'
forall(t) exists_at(y,t) -> exists_at(x,t) and 'has continuant part'(x,y,t)
entity
entity
An entity is anything that exists or has existed or will exist. (axiom label in BFO2 Reference: [001-001])
Entity
BFO 2 Reference: In all areas of empirical inquiry we encounter general terms of two sorts. First are general terms which refer to universals or types:animaltuberculosissurgical procedurediseaseSecond, are general terms used to refer to groups of entities which instantiate a given universal but do not correspond to the extension of any subuniversal of that universal because there is nothing intrinsic to the entities in question by virtue of which they – and only they – are counted as belonging to the given group. Examples are: animal purchased by the Emperortuberculosis diagnosed on a Wednesdaysurgical procedure performed on a patient from Stockholmperson identified as candidate for clinical trial #2056-555person who is signatory of Form 656-PPVpainting by Leonardo da VinciSuch terms, which represent what are called ‘specializations’ in [81
Entity doesn't have a closure axiom because the subclasses don't necessarily exhaust all possibilites. For example Werner Ceusters 'portions of reality' include 4 sorts, entities (as BFO construes them), universals, configurations, and relations. It is an open question as to whether entities as construed in BFO will at some point also include these other portions of reality. See, for example, 'How to track absolutely everything' at http://www.referent-tracking.com/_RTU/papers/CeustersICbookRevised.pdf
Julius Caesar
Verdi’s Requiem
the Second World War
your body mass index
per discussion with Barry Smith
Entity doesn't have a closure axiom because the subclasses don't necessarily exhaust all possibilites. For example Werner Ceusters 'portions of reality' include 4 sorts, entities (as BFO construes them), universals, configurations, and relations. It is an open question as to whether entities as construed in BFO will at some point also include these other portions of reality. See, for example, 'How to track absolutely everything' at http://www.referent-tracking.com/_RTU/papers/CeustersICbookRevised.pdf
An entity is anything that exists or has existed or will exist. (axiom label in BFO2 Reference: [001-001])
continuant
(forall (x) (if (Material Entity x) (exists (t) (and (TemporalRegion t) (existsAt x t))))) // axiom label in BFO2 CLIF: [011-002]
(forall (x) (if (Continuant x) (Entity x))) // axiom label in BFO2 CLIF: [008-002]
(forall (x y) (if (and (Continuant x) (exists (t) (continuantPartOfAt y x t))) (Continuant y))) // axiom label in BFO2 CLIF: [009-002]
Continuant
continuant
(forall (x y) (if (and (Continuant x) (exists (t) (hasContinuantPartOfAt y x t))) (Continuant y))) // axiom label in BFO2 CLIF: [126-001]
A continuant is an entity that persists, endures, or continues to exist through time while maintaining its identity. (axiom label in BFO2 Reference: [008-002])
BFO 2 Reference: Continuant entities are entities which can be sliced to yield parts only along the spatial dimension, yielding for example the parts of your table which we call its legs, its top, its nails. ‘My desk stretches from the window to the door. It has spatial parts, and can be sliced (in space) in two. With respect to time, however, a thing is a continuant.’ [60, p. 240
Continuant doesn't have a closure axiom because the subclasses don't necessarily exhaust all possibilites. For example, in an expansion involving bringing in some of Ceuster's other portions of reality, questions are raised as to whether universals are continuants
if b is a continuant and if, for some t, c has_continuant_part b at t, then c is a continuant. (axiom label in BFO2 Reference: [126-001])
if b is a continuant and if, for some t, cis continuant_part of b at t, then c is a continuant. (axiom label in BFO2 Reference: [009-002])
if b is a material entity, then there is some temporal interval (referred to below as a one-dimensional temporal region) during which b exists. (axiom label in BFO2 Reference: [011-002])
(forall (x) (if (Material Entity x) (exists (t) (and (TemporalRegion t) (existsAt x t))))) // axiom label in BFO2 CLIF: [011-002]
(forall (x y) (if (and (Continuant x) (exists (t) (continuantPartOfAt y x t))) (Continuant y))) // axiom label in BFO2 CLIF: [009-002]
(forall (x y) (if (and (Continuant x) (exists (t) (hasContinuantPartOfAt y x t))) (Continuant y))) // axiom label in BFO2 CLIF: [126-001]
if b is a material entity, then there is some temporal interval (referred to below as a one-dimensional temporal region) during which b exists. (axiom label in BFO2 Reference: [011-002])
if b is a continuant and if, for some t, c has_continuant_part b at t, then c is a continuant. (axiom label in BFO2 Reference: [126-001])
A continuant is an entity that persists, endures, or continues to exist through time while maintaining its identity. (axiom label in BFO2 Reference: [008-002])
Continuant doesn't have a closure axiom because the subclasses don't necessarily exhaust all possibilites. For example, in an expansion involving bringing in some of Ceuster's other portions of reality, questions are raised as to whether universals are continuants
(forall (x) (if (Continuant x) (Entity x))) // axiom label in BFO2 CLIF: [008-002]
if b is a continuant and if, for some t, cis continuant_part of b at t, then c is a continuant. (axiom label in BFO2 Reference: [009-002])
occurrent
Occurrent
(forall (x) (iff (Occurrent x) (and (Entity x) (exists (y) (temporalPartOf y x))))) // axiom label in BFO2 CLIF: [079-001]
occurrent
(forall (x) (if (Occurrent x) (exists (r) (and (SpatioTemporalRegion r) (occupiesSpatioTemporalRegion x r))))) // axiom label in BFO2 CLIF: [108-001]
An occurrent is an entity that unfolds itself in time or it is the instantaneous boundary of such an entity (for example a beginning or an ending) or it is a temporal or spatiotemporal region which such an entity occupies_temporal_region or occupies_spatiotemporal_region. (axiom label in BFO2 Reference: [077-002])
BFO 2 Reference: every occurrent that is not a temporal or spatiotemporal region is s-dependent on some independent continuant that is not a spatial region
BFO 2 Reference: s-dependence obtains between every process and its participants in the sense that, as a matter of necessity, this process could not have existed unless these or those participants existed also. A process may have a succession of participants at different phases of its unfolding. Thus there may be different players on the field at different times during the course of a football game; but the process which is the entire game s-depends_on all of these players nonetheless. Some temporal parts of this process will s-depend_on on only some of the players.
Every occurrent occupies_spatiotemporal_region some spatiotemporal region. (axiom label in BFO2 Reference: [108-001])
Occurrent doesn't have a closure axiom because the subclasses don't necessarily exhaust all possibilites. An example would be the sum of a process and the process boundary of another process.
Simons uses different terminology for relations of occurrents to regions: Denote the spatio-temporal location of a given occurrent e by 'spn[e]' and call this region its span. We may say an occurrent is at its span, in any larger region, and covers any smaller region. Now suppose we have fixed a frame of reference so that we can speak not merely of spatio-temporal but also of spatial regions (places) and temporal regions (times). The spread of an occurrent, (relative to a frame of reference) is the space it exactly occupies, and its spell is likewise the time it exactly occupies. We write 'spr[e]' and `spl[e]' respectively for the spread and spell of e, omitting mention of the frame.
b is an occurrent entity iff b is an entity that has temporal parts. (axiom label in BFO2 Reference: [079-001])
Simons uses different terminology for relations of occurrents to regions: Denote the spatio-temporal location of a given occurrent e by 'spn[e]' and call this region its span. We may say an occurrent is at its span, in any larger region, and covers any smaller region. Now suppose we have fixed a frame of reference so that we can speak not merely of spatio-temporal but also of spatial regions (places) and temporal regions (times). The spread of an occurrent, (relative to a frame of reference) is the space it exactly occupies, and its spell is likewise the time it exactly occupies. We write 'spr[e]' and `spl[e]' respectively for the spread and spell of e, omitting mention of the frame.
An occurrent is an entity that unfolds itself in time or it is the instantaneous boundary of such an entity (for example a beginning or an ending) or it is a temporal or spatiotemporal region which such an entity occupies_temporal_region or occupies_spatiotemporal_region. (axiom label in BFO2 Reference: [077-002])
per discussion with Barry Smith
Occurrent doesn't have a closure axiom because the subclasses don't necessarily exhaust all possibilites. An example would be the sum of a process and the process boundary of another process.
b is an occurrent entity iff b is an entity that has temporal parts. (axiom label in BFO2 Reference: [079-001])
(forall (x) (iff (Occurrent x) (and (Entity x) (exists (y) (temporalPartOf y x))))) // axiom label in BFO2 CLIF: [079-001]
Every occurrent occupies_spatiotemporal_region some spatiotemporal region. (axiom label in BFO2 Reference: [108-001])
(forall (x) (if (Occurrent x) (exists (r) (and (SpatioTemporalRegion r) (occupiesSpatioTemporalRegion x r))))) // axiom label in BFO2 CLIF: [108-001]
independent continuant
(forall (x t) (if (and (IndependentContinuant x) (existsAt x t)) (exists (y) (and (Entity y) (specificallyDependsOnAt y x t))))) // axiom label in BFO2 CLIF: [018-002]
(forall (x t) (if (IndependentContinuant x) (exists (r) (and (SpatialRegion r) (locatedInAt x r t))))) // axiom label in BFO2 CLIF: [134-001]
(iff (IndependentContinuant a) (and (Continuant a) (not (exists (b t) (specificallyDependsOnAt a b t))))) // axiom label in BFO2 CLIF: [017-002]
For any independent continuant b and any time t there is some spatial region r such that b is located_in r at t. (axiom label in BFO2 Reference: [134-001])
For every independent continuant b and time t during the region of time spanned by its life, there are entities which s-depends_on b during t. (axiom label in BFO2 Reference: [018-002])
ic
IndependentContinuant
a chair
a heart
a leg
a molecule
a spatial region
an atom
an orchestra.
an organism
b is an independent continuant = Def. b is a continuant which is such that there is no c and no t such that b s-depends_on c at t. (axiom label in BFO2 Reference: [017-002])
the bottom right portion of a human torso
the interior of your mouth
For every independent continuant b and time t during the region of time spanned by its life, there are entities which s-depends_on b during t. (axiom label in BFO2 Reference: [018-002])
For any independent continuant b and any time t there is some spatial region r such that b is located_in r at t. (axiom label in BFO2 Reference: [134-001])
(forall (x t) (if (and (IndependentContinuant x) (existsAt x t)) (exists (y) (and (Entity y) (specificallyDependsOnAt y x t))))) // axiom label in BFO2 CLIF: [018-002]
(iff (IndependentContinuant a) (and (Continuant a) (not (exists (b t) (specificallyDependsOnAt a b t))))) // axiom label in BFO2 CLIF: [017-002]
(forall (x t) (if (IndependentContinuant x) (exists (r) (and (SpatialRegion r) (locatedInAt x r t))))) // axiom label in BFO2 CLIF: [134-001]
b is an independent continuant = Def. b is a continuant which is such that there is no c and no t such that b s-depends_on c at t. (axiom label in BFO2 Reference: [017-002])
spatial region
true
true
(forall (x y t) (if (and (SpatialRegion x) (continuantPartOfAt y x t)) (SpatialRegion y))) // axiom label in BFO2 CLIF: [036-001]
SpatialRegion
(forall (x) (if (SpatialRegion x) (Continuant x))) // axiom label in BFO2 CLIF: [035-001]
s-region
A spatial region is a continuant entity that is a continuant_part_of spaceR as defined relative to some frame R. (axiom label in BFO2 Reference: [035-001])
All continuant parts of spatial regions are spatial regions. (axiom label in BFO2 Reference: [036-001])
BFO 2 Reference: Spatial regions do not participate in processes.
Spatial region doesn't have a closure axiom because the subclasses don't exhaust all possibilites. An example would be the union of a spatial point and a spatial line that doesn't overlap the point, or two spatial lines that intersect at a single point. In both cases the resultant spatial region is neither 0-dimensional, 1-dimensional, 2-dimensional, or 3-dimensional.
true
(forall (x y t) (if (and (SpatialRegion x) (continuantPartOfAt y x t)) (SpatialRegion y))) // axiom label in BFO2 CLIF: [036-001]
All continuant parts of spatial regions are spatial regions. (axiom label in BFO2 Reference: [036-001])
A spatial region is a continuant entity that is a continuant_part_of spaceR as defined relative to some frame R. (axiom label in BFO2 Reference: [035-001])
(forall (x) (if (SpatialRegion x) (Continuant x))) // axiom label in BFO2 CLIF: [035-001]
Spatial region doesn't have a closure axiom because the subclasses don't exhaust all possibilites. An example would be the union of a spatial point and a spatial line that doesn't overlap the point, or two spatial lines that intersect at a single point. In both cases the resultant spatial region is neither 0-dimensional, 1-dimensional, 2-dimensional, or 3-dimensional.
per discussion with Barry Smith
true
temporal region
true
true
(forall (x) (if (TemporalRegion x) (Occurrent x))) // axiom label in BFO2 CLIF: [100-001]
t-region
(forall (x y) (if (and (TemporalRegion x) (occurrentPartOf y x)) (TemporalRegion y))) // axiom label in BFO2 CLIF: [101-001]
(forall (r) (if (TemporalRegion r) (occupiesTemporalRegion r r))) // axiom label in BFO2 CLIF: [119-002]
A temporal region is an occurrent entity that is part of time as defined relative to some reference frame. (axiom label in BFO2 Reference: [100-001])
All parts of temporal regions are temporal regions. (axiom label in BFO2 Reference: [101-001])
Temporal region doesn't have a closure axiom because the subclasses don't exhaust all possibilites. An example would be the mereological sum of a temporal instant and a temporal interval that doesn't overlap the instant. In this case the resultant temporal region is neither 0-dimensional nor 1-dimensional
TemporalRegion
Every temporal region t is such that t occupies_temporal_region t. (axiom label in BFO2 Reference: [119-002])
(forall (r) (if (TemporalRegion r) (occupiesTemporalRegion r r))) // axiom label in BFO2 CLIF: [119-002]
(forall (x y) (if (and (TemporalRegion x) (occurrentPartOf y x)) (TemporalRegion y))) // axiom label in BFO2 CLIF: [101-001]
true
Every temporal region t is such that t occupies_temporal_region t. (axiom label in BFO2 Reference: [119-002])
All parts of temporal regions are temporal regions. (axiom label in BFO2 Reference: [101-001])
(forall (x) (if (TemporalRegion x) (Occurrent x))) // axiom label in BFO2 CLIF: [100-001]
true
per discussion with Barry Smith
Temporal region doesn't have a closure axiom because the subclasses don't exhaust all possibilites. An example would be the mereological sum of a temporal instant and a temporal interval that doesn't overlap the instant. In this case the resultant temporal region is neither 0-dimensional nor 1-dimensional
A temporal region is an occurrent entity that is part of time as defined relative to some reference frame. (axiom label in BFO2 Reference: [100-001])
two-dimensional spatial region
(forall (x) (if (TwoDimensionalSpatialRegion x) (SpatialRegion x))) // axiom label in BFO2 CLIF: [039-001]
TwoDimensionalSpatialRegion
2d-s-region
A two-dimensional spatial region is a spatial region that is of two dimensions. (axiom label in BFO2 Reference: [039-001])
an infinitely thin plane in space.
the surface of a sphere-shaped part of space
A two-dimensional spatial region is a spatial region that is of two dimensions. (axiom label in BFO2 Reference: [039-001])
(forall (x) (if (TwoDimensionalSpatialRegion x) (SpatialRegion x))) // axiom label in BFO2 CLIF: [039-001]
spatiotemporal region
true
true
(forall (r) (if (SpatioTemporalRegion r) (occupiesSpatioTemporalRegion r r))) // axiom label in BFO2 CLIF: [107-002]
(forall (x) (if (SpatioTemporalRegion x) (Occurrent x))) // axiom label in BFO2 CLIF: [095-001]
(forall (x) (if (SpatioTemporalRegion x) (exists (y) (and (TemporalRegion y) (temporallyProjectsOnto x y))))) // axiom label in BFO2 CLIF: [098-001]
(forall (x y) (if (and (SpatioTemporalRegion x) (occurrentPartOf y x)) (SpatioTemporalRegion y))) // axiom label in BFO2 CLIF: [096-001]
(forall (x t) (if (SpatioTemporalRegion x) (exists (y) (and (SpatialRegion y) (spatiallyProjectsOntoAt x y t))))) // axiom label in BFO2 CLIF: [099-001]
All parts of spatiotemporal regions are spatiotemporal regions. (axiom label in BFO2 Reference: [096-001])
Each spatiotemporal region at any time t projects_onto some spatial region at t. (axiom label in BFO2 Reference: [099-001])
Each spatiotemporal region projects_onto some temporal region. (axiom label in BFO2 Reference: [098-001])
Every spatiotemporal region occupies_spatiotemporal_region itself.
Every spatiotemporal region s is such that s occupies_spatiotemporal_region s. (axiom label in BFO2 Reference: [107-002])
SpatiotemporalRegion
st-region
A spatiotemporal region is an occurrent entity that is part of spacetime. (axiom label in BFO2 Reference: [095-001])
the spatiotemporal region occupied by a human life
the spatiotemporal region occupied by a process of cellular meiosis.
the spatiotemporal region occupied by the development of a cancer tumor
(forall (x t) (if (SpatioTemporalRegion x) (exists (y) (and (SpatialRegion y) (spatiallyProjectsOntoAt x y t))))) // axiom label in BFO2 CLIF: [099-001]
true
All parts of spatiotemporal regions are spatiotemporal regions. (axiom label in BFO2 Reference: [096-001])
(forall (x) (if (SpatioTemporalRegion x) (Occurrent x))) // axiom label in BFO2 CLIF: [095-001]
(forall (x y) (if (and (SpatioTemporalRegion x) (occurrentPartOf y x)) (SpatioTemporalRegion y))) // axiom label in BFO2 CLIF: [096-001]
true
A spatiotemporal region is an occurrent entity that is part of spacetime. (axiom label in BFO2 Reference: [095-001])
Every spatiotemporal region s is such that s occupies_spatiotemporal_region s. (axiom label in BFO2 Reference: [107-002])
Each spatiotemporal region projects_onto some temporal region. (axiom label in BFO2 Reference: [098-001])
(forall (r) (if (SpatioTemporalRegion r) (occupiesSpatioTemporalRegion r r))) // axiom label in BFO2 CLIF: [107-002]
(forall (x) (if (SpatioTemporalRegion x) (exists (y) (and (TemporalRegion y) (temporallyProjectsOnto x y))))) // axiom label in BFO2 CLIF: [098-001]
Each spatiotemporal region at any time t projects_onto some spatial region at t. (axiom label in BFO2 Reference: [099-001])
process
process
Process
(iff (Process a) (and (Occurrent a) (exists (b) (properTemporalPartOf b a)) (exists (c t) (and (MaterialEntity c) (specificallyDependsOnAt a c t))))) // axiom label in BFO2 CLIF: [083-003]
BFO 2 Reference: The realm of occurrents is less pervasively marked by the presence of natural units than is the case in the realm of independent continuants. Thus there is here no counterpart of ‘object’. In BFO 1.0 ‘process’ served as such a counterpart. In BFO 2.0 ‘process’ is, rather, the occurrent counterpart of ‘material entity’. Those natural – as contrasted with engineered, which here means: deliberately executed – units which do exist in the realm of occurrents are typically either parasitic on the existence of natural units on the continuant side, or they are fiat in nature. Thus we can count lives; we can count football games; we can count chemical reactions performed in experiments or in chemical manufacturing. We cannot count the processes taking place, for instance, in an episode of insect mating behavior.Even where natural units are identifiable, for example cycles in a cyclical process such as the beating of a heart or an organism’s sleep/wake cycle, the processes in question form a sequence with no discontinuities (temporal gaps) of the sort that we find for instance where billiard balls or zebrafish or planets are separated by clear spatial gaps. Lives of organisms are process units, but they too unfold in a continuous series from other, prior processes such as fertilization, and they unfold in turn in continuous series of post-life processes such as post-mortem decay. Clear examples of boundaries of processes are almost always of the fiat sort (midnight, a time of death as declared in an operating theater or on a death certificate, the initiation of a state of war)
a process of cell-division, \ a beating of the heart
a process of meiosis
a process of sleeping
p is a process = Def. p is an occurrent that has temporal proper parts and for some time t, p s-depends_on some material entity at t. (axiom label in BFO2 Reference: [083-003])
the course of a disease
the flight of a bird
the life of an organism
your process of aging.
p is a process = Def. p is an occurrent that has temporal proper parts and for some time t, p s-depends_on some material entity at t. (axiom label in BFO2 Reference: [083-003])
(iff (Process a) (and (Occurrent a) (exists (b) (properTemporalPartOf b a)) (exists (c t) (and (MaterialEntity c) (specificallyDependsOnAt a c t))))) // axiom label in BFO2 CLIF: [083-003]
disposition
disposition
Disposition
(forall (x t) (if (and (RealizableEntity x) (existsAt x t)) (exists (y) (and (MaterialEntity y) (specificallyDepends x y t))))) // axiom label in BFO2 CLIF: [063-002]
(forall (x) (if (Disposition x) (and (RealizableEntity x) (exists (y) (and (MaterialEntity y) (bearerOfAt x y t)))))) // axiom label in BFO2 CLIF: [062-002]
BFO 2 Reference: Dispositions exist along a strength continuum. Weaker forms of disposition are realized in only a fraction of triggering cases. These forms occur in a significant number of cases of a similar type [89
If b is a realizable entity then for all t at which b exists, b s-depends_on some material entity at t. (axiom label in BFO2 Reference: [063-002])
an atom of element X has the disposition to decay to an atom of element Y
b is a disposition means: b is a realizable entity & b’s bearer is some material entity & b is such that if it ceases to exist, then its bearer is physically changed, & b’s realization occurs when and because this bearer is in some special physical circumstances, & this realization occurs in virtue of the bearer’s physical make-up. (axiom label in BFO2 Reference: [062-002])
certain people have a predisposition to colon cancer
children are innately disposed to categorize objects in certain ways.
the cell wall is disposed to filter chemicals in endocitosis and exocitosis
(forall (x) (if (Disposition x) (and (RealizableEntity x) (exists (y) (and (MaterialEntity y) (bearerOfAt x y t)))))) // axiom label in BFO2 CLIF: [062-002]
b is a disposition means: b is a realizable entity & b’s bearer is some material entity & b is such that if it ceases to exist, then its bearer is physically changed, & b’s realization occurs when and because this bearer is in some special physical circumstances, & this realization occurs in virtue of the bearer’s physical make-up. (axiom label in BFO2 Reference: [062-002])
If b is a realizable entity then for all t at which b exists, b s-depends_on some material entity at t. (axiom label in BFO2 Reference: [063-002])
(forall (x t) (if (and (RealizableEntity x) (existsAt x t)) (exists (y) (and (MaterialEntity y) (specificallyDepends x y t))))) // axiom label in BFO2 CLIF: [063-002]
realizable entity
(forall (x t) (if (RealizableEntity x) (exists (y) (and (IndependentContinuant y) (not (SpatialRegion y)) (bearerOfAt y x t))))) // axiom label in BFO2 CLIF: [060-002]
(forall (x) (if (RealizableEntity x) (and (SpecificallyDependentContinuant x) (exists (y) (and (IndependentContinuant y) (not (SpatialRegion y)) (inheresIn x y)))))) // axiom label in BFO2 CLIF: [058-002]
RealizableEntity
All realizable dependent continuants have independent continuants that are not spatial regions as their bearers. (axiom label in BFO2 Reference: [060-002])
To say that b is a realizable entity is to say that b is a specifically dependent continuant that inheres in some independent continuant which is not a spatial region and is of a type instances of which are realized in processes of a correlated type. (axiom label in BFO2 Reference: [058-002])
realizable
the disposition of this piece of metal to conduct electricity.
the disposition of your blood to coagulate
the function of your reproductive organs
the role of being a doctor
the role of this boundary to delineate where Utah and Colorado meet
(forall (x t) (if (RealizableEntity x) (exists (y) (and (IndependentContinuant y) (not (SpatialRegion y)) (bearerOfAt y x t))))) // axiom label in BFO2 CLIF: [060-002]
To say that b is a realizable entity is to say that b is a specifically dependent continuant that inheres in some independent continuant which is not a spatial region and is of a type instances of which are realized in processes of a correlated type. (axiom label in BFO2 Reference: [058-002])
(forall (x) (if (RealizableEntity x) (and (SpecificallyDependentContinuant x) (exists (y) (and (IndependentContinuant y) (not (SpatialRegion y)) (inheresIn x y)))))) // axiom label in BFO2 CLIF: [058-002]
All realizable dependent continuants have independent continuants that are not spatial regions as their bearers. (axiom label in BFO2 Reference: [060-002])
zero-dimensional spatial region
ZeroDimensionalSpatialRegion
(forall (x) (if (ZeroDimensionalSpatialRegion x) (SpatialRegion x))) // axiom label in BFO2 CLIF: [037-001]
0d-s-region
A zero-dimensional spatial region is a point in space. (axiom label in BFO2 Reference: [037-001])
A zero-dimensional spatial region is a point in space. (axiom label in BFO2 Reference: [037-001])
(forall (x) (if (ZeroDimensionalSpatialRegion x) (SpatialRegion x))) // axiom label in BFO2 CLIF: [037-001]
quality
(forall (x) (if (exists (t) (and (existsAt x t) (Quality x))) (forall (t_1) (if (existsAt x t_1) (Quality x))))) // axiom label in BFO2 CLIF: [105-001]
Quality
(forall (x) (if (Quality x) (SpecificallyDependentContinuant x))) // axiom label in BFO2 CLIF: [055-001]
quality
If an entity is a quality at any time that it exists, then it is a quality at every time that it exists. (axiom label in BFO2 Reference: [105-001])
a quality is a specifically dependent continuant that, in contrast to roles and dispositions, does not require any further process in order to be realized. (axiom label in BFO2 Reference: [055-001])
the ambient temperature of this portion of air
the color of a tomato
the length of the circumference of your waist
the mass of this piece of gold.
the shape of your nose
the shape of your nostril
(forall (x) (if (Quality x) (SpecificallyDependentContinuant x))) // axiom label in BFO2 CLIF: [055-001]
(forall (x) (if (exists (t) (and (existsAt x t) (Quality x))) (forall (t_1) (if (existsAt x t_1) (Quality x))))) // axiom label in BFO2 CLIF: [105-001]
a quality is a specifically dependent continuant that, in contrast to roles and dispositions, does not require any further process in order to be realized. (axiom label in BFO2 Reference: [055-001])
If an entity is a quality at any time that it exists, then it is a quality at every time that it exists. (axiom label in BFO2 Reference: [105-001])
specifically dependent continuant
(iff (SpecificallyDependentContinuant a) (and (Continuant a) (forall (t) (if (existsAt a t) (exists (b) (and (IndependentContinuant b) (not (SpatialRegion b)) (specificallyDependsOnAt a b t))))))) // axiom label in BFO2 CLIF: [050-003]
sdc
(iff (RelationalSpecificallyDependentContinuant a) (and (SpecificallyDependentContinuant a) (forall (t) (exists (b c) (and (not (SpatialRegion b)) (not (SpatialRegion c)) (not (= b c)) (not (exists (d) (and (continuantPartOfAt d b t) (continuantPartOfAt d c t)))) (specificallyDependsOnAt a b t) (specificallyDependsOnAt a c t)))))) // axiom label in BFO2 CLIF: [131-004]
Reciprocal specifically dependent continuants: the function of this key to open this lock and the mutually dependent disposition of this lock: to be opened by this key
Specifically dependent continuant doesn't have a closure axiom because the subclasses don't necessarily exhaust all possibilites. We're not sure what else will develop here, but for example there are questions such as what are promises, obligation, etc.
SpecificallyDependentContinuant
b is a relational specifically dependent continuant = Def. b is a specifically dependent continuant and there are n > 1 independent continuants c1, … cn which are not spatial regions are such that for all 1 i < j n, ci and cj share no common parts, are such that for each 1 i n, b s-depends_on ci at every time t during the course of b’s existence (axiom label in BFO2 Reference: [131-004])
b is a specifically dependent continuant = Def. b is a continuant & there is some independent continuant c which is not a spatial region and which is such that b s-depends_on c at every time t during the course of b’s existence. (axiom label in BFO2 Reference: [050-003])
of one-sided specifically dependent continuants: the mass of this tomato
of relational dependent continuants (multiple bearers): John’s love for Mary, the ownership relation between John and this statue, the relation of authority between John and his subordinates.
the disposition of this fish to decay
the function of this heart: to pump blood
the mutual dependence of proton donors and acceptors in chemical reactions [79
the mutual dependence of the role predator and the role prey as played by two organisms in a given interaction
the pink color of a medium rare piece of grilled filet mignon at its center
the role of being a doctor
the shape of this hole.
the smell of this portion of mozzarella
b is a specifically dependent continuant = Def. b is a continuant & there is some independent continuant c which is not a spatial region and which is such that b s-depends_on c at every time t during the course of b’s existence. (axiom label in BFO2 Reference: [050-003])
(iff (SpecificallyDependentContinuant a) (and (Continuant a) (forall (t) (if (existsAt a t) (exists (b) (and (IndependentContinuant b) (not (SpatialRegion b)) (specificallyDependsOnAt a b t))))))) // axiom label in BFO2 CLIF: [050-003]
(iff (RelationalSpecificallyDependentContinuant a) (and (SpecificallyDependentContinuant a) (forall (t) (exists (b c) (and (not (SpatialRegion b)) (not (SpatialRegion c)) (not (= b c)) (not (exists (d) (and (continuantPartOfAt d b t) (continuantPartOfAt d c t)))) (specificallyDependsOnAt a b t) (specificallyDependsOnAt a c t)))))) // axiom label in BFO2 CLIF: [131-004]
b is a relational specifically dependent continuant = Def. b is a specifically dependent continuant and there are n > 1 independent continuants c1, … cn which are not spatial regions are such that for all 1 i < j n, ci and cj share no common parts, are such that for each 1 i n, b s-depends_on ci at every time t during the course of b’s existence (axiom label in BFO2 Reference: [131-004])
Specifically dependent continuant doesn't have a closure axiom because the subclasses don't necessarily exhaust all possibilites. We're not sure what else will develop here, but for example there are questions such as what are promises, obligation, etc.
per discussion with Barry Smith
role
role
(forall (x) (if (Role x) (RealizableEntity x))) // axiom label in BFO2 CLIF: [061-001]
BFO 2 Reference: One major family of examples of non-rigid universals involves roles, and ontologies developed for corresponding administrative purposes may consist entirely of representatives of entities of this sort. Thus ‘professor’, defined as follows,b instance_of professor at t =Def. there is some c, c instance_of professor role & c inheres_in b at t.denotes a non-rigid universal and so also do ‘nurse’, ‘student’, ‘colonel’, ‘taxpayer’, and so forth. (These terms are all, in the jargon of philosophy, phase sortals.) By using role terms in definitions, we can create a BFO conformant treatment of such entities drawing on the fact that, while an instance of professor may be simultaneously an instance of trade union member, no instance of the type professor role is also (at any time) an instance of the type trade union member role (any more than any instance of the type color is at any time an instance of the type length).If an ontology of employment positions should be defined in terms of roles following the above pattern, this enables the ontology to do justice to the fact that individuals instantiate the corresponding universals – professor, sergeant, nurse – only during certain phases in their lives.
John’s role of husband to Mary is dependent on Mary’s role of wife to John, and both are dependent on the object aggregate comprising John and Mary as member parts joined together through the relational quality of being married.
Role
b is a role means: b is a realizable entity & b exists because there is some single bearer that is in some special physical, social, or institutional set of circumstances in which this bearer does not have to be& b is not such that, if it ceases to exist, then the physical make-up of the bearer is thereby changed. (axiom label in BFO2 Reference: [061-001])
the priest role
the role of a boundary to demarcate two neighboring administrative territories
the role of a building in serving as a military target
the role of a stone in marking a property boundary
the role of subject in a clinical trial
the student role
(forall (x) (if (Role x) (RealizableEntity x))) // axiom label in BFO2 CLIF: [061-001]
b is a role means: b is a realizable entity & b exists because there is some single bearer that is in some special physical, social, or institutional set of circumstances in which this bearer does not have to be& b is not such that, if it ceases to exist, then the physical make-up of the bearer is thereby changed. (axiom label in BFO2 Reference: [061-001])
fiat object
(forall (x) (if (FiatObjectPart x) (and (MaterialEntity x) (forall (t) (if (existsAt x t) (exists (y) (and (Object y) (properContinuantPartOfAt x y t)))))))) // axiom label in BFO2 CLIF: [027-004]
BFO 2 Reference: Most examples of fiat object parts are associated with theoretically drawn divisions
FiatObjectPart
b is a fiat object part = Def. b is a material entity which is such that for all times t, if b exists at t then there is some object c such that b proper continuant_part of c at t and c is demarcated from the remainder of c by a two-dimensional continuant fiat boundary. (axiom label in BFO2 Reference: [027-004])
fiat-object
or with divisions drawn by cognitive subjects for practical reasons, such as the division of a cake (before slicing) into (what will become) slices (and thus member parts of an object aggregate). However, this does not mean that fiat object parts are dependent for their existence on divisions or delineations effected by cognitive subjects. If, for example, it is correct to conceive geological layers of the Earth as fiat object parts of the Earth, then even though these layers were first delineated in recent times, still existed long before such delineation and what holds of these layers (for example that the oldest layers are also the lowest layers) did not begin to hold because of our acts of delineation.Treatment of material entity in BFOExamples viewed by some as problematic cases for the trichotomy of fiat object part, object, and object aggregate include: a mussel on (and attached to) a rock, a slime mold, a pizza, a cloud, a galaxy, a railway train with engine and multiple carriages, a clonal stand of quaking aspen, a bacterial community (biofilm), a broken femur. Note that, as Aristotle already clearly recognized, such problematic cases – which lie at or near the penumbra of instances defined by the categories in question – need not invalidate these categories. The existence of grey objects does not prove that there are not objects which are black and objects which are white; the existence of mules does not prove that there are not objects which are donkeys and objects which are horses. It does, however, show that the examples in question need to be addressed carefully in order to show how they can be fitted into the proposed scheme, for example by recognizing additional subdivisions [29
the FMA:regional parts of an intact human body.
the Western hemisphere of the Earth
the division of the brain into regions
the division of the planet into hemispheres
the dorsal and ventral surfaces of the body
the upper and lower lobes of the left lung
(forall (x) (if (FiatObjectPart x) (and (MaterialEntity x) (forall (t) (if (existsAt x t) (exists (y) (and (Object y) (properContinuantPartOfAt x y t)))))))) // axiom label in BFO2 CLIF: [027-004]
b is a fiat object part = Def. b is a material entity which is such that for all times t, if b exists at t then there is some object c such that b proper continuant_part of c at t and c is demarcated from the remainder of c by a two-dimensional continuant fiat boundary. (axiom label in BFO2 Reference: [027-004])
one-dimensional spatial region
(forall (x) (if (OneDimensionalSpatialRegion x) (SpatialRegion x))) // axiom label in BFO2 CLIF: [038-001]
OneDimensionalSpatialRegion
1d-s-region
A one-dimensional spatial region is a line or aggregate of lines stretching from one point in space to another. (axiom label in BFO2 Reference: [038-001])
an edge of a cube-shaped portion of space.
(forall (x) (if (OneDimensionalSpatialRegion x) (SpatialRegion x))) // axiom label in BFO2 CLIF: [038-001]
A one-dimensional spatial region is a line or aggregate of lines stretching from one point in space to another. (axiom label in BFO2 Reference: [038-001])
object aggregate
object-aggregate
ObjectAggregate
ISBN:978-3-938793-98-5pp124-158#Thomas Bittner and Barry Smith, 'A Theory of Granular Partitions', in K. Munn and B. Smith (eds.), Applied Ontology: An Introduction, Frankfurt/Lancaster: ontos, 2008, 125-158.
(forall (x) (if (ObjectAggregate x) (and (MaterialEntity x) (forall (t) (if (existsAt x t) (exists (y z) (and (Object y) (Object z) (memberPartOfAt y x t) (memberPartOfAt z x t) (not (= y z)))))) (not (exists (w t_1) (and (memberPartOfAt w x t_1) (not (Object w)))))))) // axiom label in BFO2 CLIF: [025-004]
An entity a is an object aggregate if and only if there is a mutually exhaustive and pairwise disjoint partition of a into objects
BFO 2 Reference: object aggregates may gain and lose parts while remaining numerically identical (one and the same individual) over time. This holds both for aggregates whose membership is determined naturally (the aggregate of cells in your body) and aggregates determined by fiat (a baseball team, a congressional committee).
a collection of cells in a blood biobank.
a swarm of bees is an aggregate of members who are linked together through natural bonds
a symphony orchestra
an organization is an aggregate whose member parts have roles of specific types (for example in a jazz band, a chess club, a football team)
b is an object aggregate means: b is a material entity consisting exactly of a plurality of objects as member_parts at all times at which b exists. (axiom label in BFO2 Reference: [025-004])
defined by fiat: the aggregate of members of an organization
defined through physical attachment: the aggregate of atoms in a lump of granite
defined through physical containment: the aggregate of molecules of carbon dioxide in a sealed container
defined via attributive delimitations such as: the patients in this hospital
the aggregate of bearings in a constant velocity axle joint
the aggregate of blood cells in your body
the nitrogen atoms in the atmosphere
the restaurants in Palo Alto
your collection of Meissen ceramic plates.
b is an object aggregate means: b is a material entity consisting exactly of a plurality of objects as member_parts at all times at which b exists. (axiom label in BFO2 Reference: [025-004])
An entity a is an object aggregate if and only if there is a mutually exhaustive and pairwise disjoint partition of a into objects
ISBN:978-3-938793-98-5pp124-158#Thomas Bittner and Barry Smith, 'A Theory of Granular Partitions', in K. Munn and B. Smith (eds.), Applied Ontology: An Introduction, Frankfurt/Lancaster: ontos, 2008, 125-158.
An entity a is an object aggregate if and only if there is a mutually exhaustive and pairwise disjoint partition of a into objects
(forall (x) (if (ObjectAggregate x) (and (MaterialEntity x) (forall (t) (if (existsAt x t) (exists (y z) (and (Object y) (Object z) (memberPartOfAt y x t) (memberPartOfAt z x t) (not (= y z)))))) (not (exists (w t_1) (and (memberPartOfAt w x t_1) (not (Object w)))))))) // axiom label in BFO2 CLIF: [025-004]
three-dimensional spatial region
(forall (x) (if (ThreeDimensionalSpatialRegion x) (SpatialRegion x))) // axiom label in BFO2 CLIF: [040-001]
3d-s-region
ThreeDimensionalSpatialRegion
A three-dimensional spatial region is a spatial region that is of three dimensions. (axiom label in BFO2 Reference: [040-001])
a cube-shaped region of space
a sphere-shaped region of space,
A three-dimensional spatial region is a spatial region that is of three dimensions. (axiom label in BFO2 Reference: [040-001])
(forall (x) (if (ThreeDimensionalSpatialRegion x) (SpatialRegion x))) // axiom label in BFO2 CLIF: [040-001]
site
Site
(forall (x) (if (Site x) (ImmaterialEntity x))) // axiom label in BFO2 CLIF: [034-002]
a hole in the interior of a portion of cheese
a rabbit hole
an air traffic control region defined in the airspace above an airport
b is a site means: b is a three-dimensional immaterial entity that is (partially or wholly) bounded by a material entity or it is a three-dimensional immaterial part thereof. (axiom label in BFO2 Reference: [034-002])
site
Manhattan Canyon)
the Grand Canyon
the Piazza San Marco
the cockpit of an aircraft
the hold of a ship
the interior of a kangaroo pouch
the interior of the trunk of your car
the interior of your bedroom
the interior of your office
the interior of your refrigerator
the lumen of your gut
your left nostril (a fiat part – the opening – of your left nasal cavity)
(forall (x) (if (Site x) (ImmaterialEntity x))) // axiom label in BFO2 CLIF: [034-002]
b is a site means: b is a three-dimensional immaterial entity that is (partially or wholly) bounded by a material entity or it is a three-dimensional immaterial part thereof. (axiom label in BFO2 Reference: [034-002])
object
Object
BFO 2 Reference: Each object is such that there are entities of which we can assert unproblematically that they lie in its interior, and other entities of which we can assert unproblematically that they lie in its exterior. This may not be so for entities lying at or near the boundary between the interior and exterior. This means that two objects – for example the two cells depicted in Figure 3 – may be such that there are material entities crossing their boundaries which belong determinately to neither cell. Something similar obtains in certain cases of conjoined twins (see below).
BFO 2 Reference: To say that b is causally unified means: b is a material entity which is such that its material parts are tied together in such a way that, in environments typical for entities of the type in question,if c, a continuant part of b that is in the interior of b at t, is larger than a certain threshold size (which will be determined differently from case to case, depending on factors such as porosity of external cover) and is moved in space to be at t at a location on the exterior of the spatial region that had been occupied by b at t, then either b’s other parts will be moved in coordinated fashion or b will be damaged (be affected, for example, by breakage or tearing) in the interval between t and t.causal changes in one part of b can have consequences for other parts of b without the mediation of any entity that lies on the exterior of b. Material entities with no proper material parts would satisfy these conditions trivially. Candidate examples of types of causal unity for material entities of more complex sorts are as follows (this is not intended to be an exhaustive list):CU1: Causal unity via physical coveringHere the parts in the interior of the unified entity are combined together causally through a common membrane or other physical covering\. The latter points outwards toward and may serve a protective function in relation to what lies on the exterior of the entity [13, 47
object
BFO 2 Reference: BFO rests on the presupposition that at multiple micro-, meso- and macroscopic scales reality exhibits certain stable, spatially separated or separable material units, combined or combinable into aggregates of various sorts (for example organisms into what are called ‘populations’). Such units play a central role in almost all domains of natural science from particle physics to cosmology. Many scientific laws govern the units in question, employing general terms (such as ‘molecule’ or ‘planet’) referring to the types and subtypes of units, and also to the types and subtypes of the processes through which such units develop and interact. The division of reality into such natural units is at the heart of biological science, as also is the fact that these units may form higher-level units (as cells form multicellular organisms) and that they may also form aggregates of units, for example as cells form portions of tissue and organs form families, herds, breeds, species, and so on. At the same time, the division of certain portions of reality into engineered units (manufactured artifacts) is the basis of modern industrial technology, which rests on the distributed mass production of engineered parts through division of labor and on their assembly into larger, compound units such as cars and laptops. The division of portions of reality into units is one starting point for the phenomenon of counting.
BFO 2 Reference: an object is a maximal causally unified material entity
BFO 2 Reference: ‘objects’ are sometimes referred to as ‘grains’ [74
atom
b is an object means: b is a material entity which manifests causal unity of one or other of the types CUn listed above & is of a type (a material universal) instances of which are maximal relative to this criterion of causal unity. (axiom label in BFO2 Reference: [024-001])
cell
cells and organisms
engineered artifacts
grain of sand
molecule
organelle
organism
planet
solid portions of matter
star
b is an object means: b is a material entity which manifests causal unity of one or other of the types CUn listed above & is of a type (a material universal) instances of which are maximal relative to this criterion of causal unity. (axiom label in BFO2 Reference: [024-001])
generically dependent continuant
gdc
GenericallyDependentContinuant
(iff (GenericallyDependentContinuant a) (and (Continuant a) (exists (b t) (genericallyDependsOnAt a b t)))) // axiom label in BFO2 CLIF: [074-001]
The entries in your database are patterns instantiated as quality instances in your hard drive. The database itself is an aggregate of such patterns. When you create the database you create a particular instance of the generically dependent continuant type database. Each entry in the database is an instance of the generically dependent continuant type IAO: information content entity.
b is a generically dependent continuant = Def. b is a continuant that g-depends_on one or more other entities. (axiom label in BFO2 Reference: [074-001])
the pdf file on your laptop, the pdf file that is a copy thereof on my laptop
the sequence of this protein molecule; the sequence that is a copy thereof in that protein molecule.
(iff (GenericallyDependentContinuant a) (and (Continuant a) (exists (b t) (genericallyDependsOnAt a b t)))) // axiom label in BFO2 CLIF: [074-001]
b is a generically dependent continuant = Def. b is a continuant that g-depends_on one or more other entities. (axiom label in BFO2 Reference: [074-001])
function
function
(forall (x) (if (Function x) (Disposition x))) // axiom label in BFO2 CLIF: [064-001]
A function is a disposition that exists in virtue of the bearer’s physical make-up and this physical make-up is something the bearer possesses because it came into being, either through evolution (in the case of natural biological entities) or through intentional design (in the case of artifacts), in order to realize processes of a certain sort. (axiom label in BFO2 Reference: [064-001])
BFO 2 Reference: In the past, we have distinguished two varieties of function, artifactual function and biological function. These are not asserted subtypes of BFO:function however, since the same function – for example: to pump, to transport – can exist both in artifacts and in biological entities. The asserted subtypes of function that would be needed in order to yield a separate monoheirarchy are not artifactual function, biological function, etc., but rather transporting function, pumping function, etc.
Function
the function of a hammer to drive in nails
the function of a heart pacemaker to regulate the beating of a heart through electricity
the function of amylase in saliva to break down starch into sugar
A function is a disposition that exists in virtue of the bearer’s physical make-up and this physical make-up is something the bearer possesses because it came into being, either through evolution (in the case of natural biological entities) or through intentional design (in the case of artifacts), in order to realize processes of a certain sort. (axiom label in BFO2 Reference: [064-001])
(forall (x) (if (Function x) (Disposition x))) // axiom label in BFO2 CLIF: [064-001]
process boundary
(iff (ProcessBoundary a) (exists (p) (and (Process p) (temporalPartOf a p) (not (exists (b) (properTemporalPartOf b a)))))) // axiom label in BFO2 CLIF: [084-001]
(forall (x) (if (ProcessBoundary x) (exists (y) (and (ZeroDimensionalTemporalRegion y) (occupiesTemporalRegion x y))))) // axiom label in BFO2 CLIF: [085-002]
Every process boundary occupies_temporal_region a zero-dimensional temporal region. (axiom label in BFO2 Reference: [085-002])
ProcessBoundary
p is a process boundary =Def. p is a temporal part of a process & p has no proper temporal parts. (axiom label in BFO2 Reference: [084-001])
p-boundary
the boundary between the 2nd and 3rd year of your life.
(iff (ProcessBoundary a) (exists (p) (and (Process p) (temporalPartOf a p) (not (exists (b) (properTemporalPartOf b a)))))) // axiom label in BFO2 CLIF: [084-001]
(forall (x) (if (ProcessBoundary x) (exists (y) (and (ZeroDimensionalTemporalRegion y) (occupiesTemporalRegion x y))))) // axiom label in BFO2 CLIF: [085-002]
Every process boundary occupies_temporal_region a zero-dimensional temporal region. (axiom label in BFO2 Reference: [085-002])
p is a process boundary =Def. p is a temporal part of a process & p has no proper temporal parts. (axiom label in BFO2 Reference: [084-001])
one-dimensional temporal region
(forall (x) (if (OneDimensionalTemporalRegion x) (TemporalRegion x))) // axiom label in BFO2 CLIF: [103-001]
1d-t-region
A one-dimensional temporal region is a temporal region that is extended. (axiom label in BFO2 Reference: [103-001])
BFO 2 Reference: A temporal interval is a special kind of one-dimensional temporal region, namely one that is self-connected (is without gaps or breaks).
OneDimensionalTemporalRegion
the temporal region during which a process occurs.
A one-dimensional temporal region is a temporal region that is extended. (axiom label in BFO2 Reference: [103-001])
(forall (x) (if (OneDimensionalTemporalRegion x) (TemporalRegion x))) // axiom label in BFO2 CLIF: [103-001]
material entity
material
(forall (x) (if (MaterialEntity x) (IndependentContinuant x))) // axiom label in BFO2 CLIF: [019-002]
MaterialEntity
(forall (x) (if (and (Entity x) (exists (y t) (and (MaterialEntity y) (continuantPartOfAt x y t)))) (MaterialEntity x))) // axiom label in BFO2 CLIF: [021-002]
(forall (x) (if (and (Entity x) (exists (y t) (and (MaterialEntity y) (continuantPartOfAt y x t)))) (MaterialEntity x))) // axiom label in BFO2 CLIF: [020-002]
A material entity is an independent continuant that has some portion of matter as proper or improper continuant part. (axiom label in BFO2 Reference: [019-002])
BFO 2 Reference: Material entities (continuants) can preserve their identity even while gaining and losing material parts. Continuants are contrasted with occurrents, which unfold themselves in successive temporal parts or phases [60
BFO 2 Reference: Object, Fiat Object Part and Object Aggregate are not intended to be exhaustive of Material Entity. Users are invited to propose new subcategories of Material Entity.
BFO 2 Reference: ‘Matter’ is intended to encompass both mass and energy (we will address the ontological treatment of portions of energy in a later version of BFO). A portion of matter is anything that includes elementary particles among its proper or improper parts: quarks and leptons, including electrons, as the smallest particles thus far discovered; baryons (including protons and neutrons) at a higher level of granularity; atoms and molecules at still higher levels, forming the cells, organs, organisms and other material entities studied by biologists, the portions of rock studied by geologists, the fossils studied by paleontologists, and so on.Material entities are three-dimensional entities (entities extended in three spatial dimensions), as contrasted with the processes in which they participate, which are four-dimensional entities (entities extended also along the dimension of time).According to the FMA, material entities may have immaterial entities as parts – including the entities identified below as sites; for example the interior (or ‘lumen’) of your small intestine is a part of your body. BFO 2.0 embodies a decision to follow the FMA here.
Every entity which has a material entity as continuant part is a material entity. (axiom label in BFO2 Reference: [020-002])
a flame
a forest fire
a human being
a hurricane
a photon
a puff of smoke
a sea wave
a tornado
an aggregate of human beings.
an energy wave
an epidemic
every entity of which a material entity is continuant part is also a material entity. (axiom label in BFO2 Reference: [021-002])
the undetached arm of a human being
(forall (x) (if (and (Entity x) (exists (y t) (and (MaterialEntity y) (continuantPartOfAt x y t)))) (MaterialEntity x))) // axiom label in BFO2 CLIF: [021-002]
(forall (x) (if (MaterialEntity x) (IndependentContinuant x))) // axiom label in BFO2 CLIF: [019-002]
every entity of which a material entity is continuant part is also a material entity. (axiom label in BFO2 Reference: [021-002])
A material entity is an independent continuant that has some portion of matter as proper or improper continuant part. (axiom label in BFO2 Reference: [019-002])
(forall (x) (if (and (Entity x) (exists (y t) (and (MaterialEntity y) (continuantPartOfAt y x t)))) (MaterialEntity x))) // axiom label in BFO2 CLIF: [020-002]
Every entity which has a material entity as continuant part is a material entity. (axiom label in BFO2 Reference: [020-002])
continuant fiat boundary
ContinuantFiatBoundary
cf-boundary
(iff (ContinuantFiatBoundary a) (and (ImmaterialEntity a) (exists (b) (and (or (ZeroDimensionalSpatialRegion b) (OneDimensionalSpatialRegion b) (TwoDimensionalSpatialRegion b)) (forall (t) (locatedInAt a b t)))) (not (exists (c t) (and (SpatialRegion c) (continuantPartOfAt c a t)))))) // axiom label in BFO2 CLIF: [029-001]
BFO 2 Reference: In BFO 1.1 the assumption was made that the external surface of a material entity such as a cell could be treated as if it were a boundary in the mathematical sense. The new document propounds the view that when we talk about external surfaces of material objects in this way then we are talking about something fiat. To be dealt with in a future version: fiat boundaries at different levels of granularity.More generally, the focus in discussion of boundaries in BFO 2.0 is now on fiat boundaries, which means: boundaries for which there is no assumption that they coincide with physical discontinuities. The ontology of boundaries becomes more closely allied with the ontology of regions.
BFO 2 Reference: a continuant fiat boundary is a boundary of some material entity (for example: the plane separating the Northern and Southern hemispheres; the North Pole), or it is a boundary of some immaterial entity (for example of some portion of airspace). Three basic kinds of continuant fiat boundary can be distinguished (together with various combination kinds [29
Continuant fiat boundary doesn't have a closure axiom because the subclasses don't necessarily exhaust all possibilites. An example would be the mereological sum of two-dimensional continuant fiat boundary and a one dimensional continuant fiat boundary that doesn't overlap it. The situation is analogous to temporal and spatial regions.
Every continuant fiat boundary is located at some spatial region at every time at which it exists
b is a continuant fiat boundary = Def. b is an immaterial entity that is of zero, one or two dimensions and does not include a spatial region as part. (axiom label in BFO2 Reference: [029-001])
Continuant fiat boundary doesn't have a closure axiom because the subclasses don't necessarily exhaust all possibilites. An example would be the mereological sum of two-dimensional continuant fiat boundary and a one dimensional continuant fiat boundary that doesn't overlap it. The situation is analogous to temporal and spatial regions.
b is a continuant fiat boundary = Def. b is an immaterial entity that is of zero, one or two dimensions and does not include a spatial region as part. (axiom label in BFO2 Reference: [029-001])
(iff (ContinuantFiatBoundary a) (and (ImmaterialEntity a) (exists (b) (and (or (ZeroDimensionalSpatialRegion b) (OneDimensionalSpatialRegion b) (TwoDimensionalSpatialRegion b)) (forall (t) (locatedInAt a b t)))) (not (exists (c t) (and (SpatialRegion c) (continuantPartOfAt c a t)))))) // axiom label in BFO2 CLIF: [029-001]
immaterial entity
ImmaterialEntity
immaterial
BFO 2 Reference: Immaterial entities are divided into two subgroups:boundaries and sites, which bound, or are demarcated in relation, to material entities, and which can thus change location, shape and size and as their material hosts move or change shape or size (for example: your nasal passage; the hold of a ship; the boundary of Wales (which moves with the rotation of the Earth) [38, 7, 10
one-dimensional continuant fiat boundary
OneDimensionalContinuantFiatBoundary
(iff (OneDimensionalContinuantFiatBoundary a) (and (ContinuantFiatBoundary a) (exists (b) (and (OneDimensionalSpatialRegion b) (forall (t) (locatedInAt a b t)))))) // axiom label in BFO2 CLIF: [032-001]
1d-cf-boundary
The Equator
a one-dimensional continuant fiat boundary is a continuous fiat line whose location is defined in relation to some material entity. (axiom label in BFO2 Reference: [032-001])
all geopolitical boundaries
all lines of latitude and longitude
the line separating the outer surface of the mucosa of the lower lip from the outer surface of the skin of the chin.
the median sulcus of your tongue
(iff (OneDimensionalContinuantFiatBoundary a) (and (ContinuantFiatBoundary a) (exists (b) (and (OneDimensionalSpatialRegion b) (forall (t) (locatedInAt a b t)))))) // axiom label in BFO2 CLIF: [032-001]
a one-dimensional continuant fiat boundary is a continuous fiat line whose location is defined in relation to some material entity. (axiom label in BFO2 Reference: [032-001])
process profile
(forall (x y) (if (processProfileOf x y) (and (properContinuantPartOf x y) (exists (z t) (and (properOccurrentPartOf z y) (TemporalRegion t) (occupiesSpatioTemporalRegion x t) (occupiesSpatioTemporalRegion y t) (occupiesSpatioTemporalRegion z t) (not (exists (w) (and (occurrentPartOf w x) (occurrentPartOf w z))))))))) // axiom label in BFO2 CLIF: [094-005]
ProcessProfile
process-profile
(iff (ProcessProfile a) (exists (b) (and (Process b) (processProfileOf a b)))) // axiom label in BFO2 CLIF: [093-002]
On a somewhat higher level of complexity are what we shall call rate process profiles, which are the targets of selective abstraction focused not on determinate quality magnitudes plotted over time, but rather on certain ratios between these magnitudes and elapsed times. A speed process profile, for example, is represented by a graph plotting against time the ratio of distance covered per unit of time. Since rates may change, and since such changes, too, may have rates of change, we have to deal here with a hierarchy of process profile universals at successive levels
One important sub-family of rate process profiles is illustrated by the beat or frequency profiles of cyclical processes, illustrated by the 60 beats per minute beating process of John’s heart, or the 120 beats per minute drumming process involved in one of John’s performances in a rock band, and so on. Each such process includes what we shall call a beat process profile instance as part, a subtype of rate process profile in which the salient ratio is not distance covered but rather number of beat cycles per unit of time. Each beat process profile instance instantiates the determinable universal beat process profile. But it also instantiates multiple more specialized universals at lower levels of generality, selected from rate process profilebeat process profileregular beat process profile3 bpm beat process profile4 bpm beat process profileirregular beat process profileincreasing beat process profileand so on.In the case of a regular beat process profile, a rate can be assigned in the simplest possible fashion by dividing the number of cycles by the length of the temporal region occupied by the beating process profile as a whole. Irregular process profiles of this sort, for example as identified in the clinic, or in the readings on an aircraft instrument panel, are often of diagnostic significance.
The simplest type of process profiles are what we shall call ‘quality process profiles’, which are the process profiles which serve as the foci of the sort of selective abstraction that is involved when measurements are made of changes in single qualities, as illustrated, for example, by process profiles of mass, temperature, aortic pressure, and so on.
b is a process_profile =Def. there is some process c such that b process_profile_of c (axiom label in BFO2 Reference: [093-002])
b process_profile_of c holds when b proper_occurrent_part_of c& there is some proper_occurrent_part d of c which has no parts in common with b & is mutually dependent on b& is such that b, c and d occupy the same temporal region (axiom label in BFO2 Reference: [094-005])
b process_profile_of c holds when b proper_occurrent_part_of c& there is some proper_occurrent_part d of c which has no parts in common with b & is mutually dependent on b& is such that b, c and d occupy the same temporal region (axiom label in BFO2 Reference: [094-005])
b is a process_profile =Def. there is some process c such that b process_profile_of c (axiom label in BFO2 Reference: [093-002])
(iff (ProcessProfile a) (exists (b) (and (Process b) (processProfileOf a b)))) // axiom label in BFO2 CLIF: [093-002]
(forall (x y) (if (processProfileOf x y) (and (properContinuantPartOf x y) (exists (z t) (and (properOccurrentPartOf z y) (TemporalRegion t) (occupiesSpatioTemporalRegion x t) (occupiesSpatioTemporalRegion y t) (occupiesSpatioTemporalRegion z t) (not (exists (w) (and (occurrentPartOf w x) (occurrentPartOf w z))))))))) // axiom label in BFO2 CLIF: [094-005]
relational quality
2
(iff (RelationalQuality a) (exists (b c t) (and (IndependentContinuant b) (IndependentContinuant c) (qualityOfAt a b t) (qualityOfAt a c t)))) // axiom label in BFO2 CLIF: [057-001]
John’s role of husband to Mary is dependent on Mary’s role of wife to John, and both are dependent on the object aggregate comprising John and Mary as member parts joined together through the relational quality of being married.
RelationalQuality
a marriage bond, an instance of love, an obligation between one person and another.
r-quality
b is a relational quality = Def. for some independent continuants c, d and for some time t: b quality_of c at t & b quality_of d at t. (axiom label in BFO2 Reference: [057-001])
(iff (RelationalQuality a) (exists (b c t) (and (IndependentContinuant b) (IndependentContinuant c) (qualityOfAt a b t) (qualityOfAt a c t)))) // axiom label in BFO2 CLIF: [057-001]
2
b is a relational quality = Def. for some independent continuants c, d and for some time t: b quality_of c at t & b quality_of d at t. (axiom label in BFO2 Reference: [057-001])
two-dimensional continuant fiat boundary
2d-cf-boundary
TwoDimensionalContinuantFiatBoundary
(iff (TwoDimensionalContinuantFiatBoundary a) (and (ContinuantFiatBoundary a) (exists (b) (and (TwoDimensionalSpatialRegion b) (forall (t) (locatedInAt a b t)))))) // axiom label in BFO2 CLIF: [033-001]
a two-dimensional continuant fiat boundary (surface) is a self-connected fiat surface whose location is defined in relation to some material entity. (axiom label in BFO2 Reference: [033-001])
(iff (TwoDimensionalContinuantFiatBoundary a) (and (ContinuantFiatBoundary a) (exists (b) (and (TwoDimensionalSpatialRegion b) (forall (t) (locatedInAt a b t)))))) // axiom label in BFO2 CLIF: [033-001]
a two-dimensional continuant fiat boundary (surface) is a self-connected fiat surface whose location is defined in relation to some material entity. (axiom label in BFO2 Reference: [033-001])
zero-dimensional continuant fiat boundary
(iff (ZeroDimensionalContinuantFiatBoundary a) (and (ContinuantFiatBoundary a) (exists (b) (and (ZeroDimensionalSpatialRegion b) (forall (t) (locatedInAt a b t)))))) // axiom label in BFO2 CLIF: [031-001]
0d-cf-boundary
ZeroDimensionalContinuantFiatBoundary
a zero-dimensional continuant fiat boundary is a fiat point whose location is defined in relation to some material entity. (axiom label in BFO2 Reference: [031-001])
the geographic North Pole
the point of origin of some spatial coordinate system.
the quadripoint where the boundaries of Colorado, Utah, New Mexico, and Arizona meet
zero dimension continuant fiat boundaries are not spatial points. Considering the example 'the quadripoint where the boundaries of Colorado, Utah, New Mexico, and Arizona meet' : There are many frames in which that point is zooming through many points in space. Whereas, no matter what the frame, the quadripoint is always in the same relation to the boundaries of Colorado, Utah, New Mexico, and Arizona.
a zero-dimensional continuant fiat boundary is a fiat point whose location is defined in relation to some material entity. (axiom label in BFO2 Reference: [031-001])
(iff (ZeroDimensionalContinuantFiatBoundary a) (and (ContinuantFiatBoundary a) (exists (b) (and (ZeroDimensionalSpatialRegion b) (forall (t) (locatedInAt a b t)))))) // axiom label in BFO2 CLIF: [031-001]
requested by Melanie Courtot
zero dimension continuant fiat boundaries are not spatial points. Considering the example 'the quadripoint where the boundaries of Colorado, Utah, New Mexico, and Arizona meet' : There are many frames in which that point is zooming through many points in space. Whereas, no matter what the frame, the quadripoint is always in the same relation to the boundaries of Colorado, Utah, New Mexico, and Arizona.
zero-dimensional temporal region
0d-t-region
(forall (x) (if (ZeroDimensionalTemporalRegion x) (TemporalRegion x))) // axiom label in BFO2 CLIF: [102-001]
A zero-dimensional temporal region is a temporal region that is without extent. (axiom label in BFO2 Reference: [102-001])
ZeroDimensionalTemporalRegion
a temporal region that is occupied by a process boundary
right now
temporal instant.
the moment at which a child is born
the moment at which a finger is detached in an industrial accident
the moment of death.
(forall (x) (if (ZeroDimensionalTemporalRegion x) (TemporalRegion x))) // axiom label in BFO2 CLIF: [102-001]
A zero-dimensional temporal region is a temporal region that is without extent. (axiom label in BFO2 Reference: [102-001])
history
A history is a process that is the sum of the totality of processes taking place in the spatiotemporal region occupied by a material entity or site, including processes on the surface of the entity or within the cavities to which it serves as host. (axiom label in BFO2 Reference: [138-001])
History
history
A history is a process that is the sum of the totality of processes taking place in the spatiotemporal region occupied by a material entity or site, including processes on the surface of the entity or within the cavities to which it serves as host. (axiom label in BFO2 Reference: [138-001])
Person:Alan Ruttenberg
To say that each spatiotemporal region s temporally_projects_onto some temporal region t is to say that t is the temporal extension of s. (axiom label in BFO2 Reference: [080-003])
To say that spatiotemporal region s spatially_projects_onto spatial region r at t is to say that r is the spatial extent of s at t. (axiom label in BFO2 Reference: [081-003])
To say that each spatiotemporal region s temporally_projects_onto some temporal region t is to say that t is the temporal extension of s. (axiom label in BFO2 Reference: [080-003])
To say that spatiotemporal region s spatially_projects_onto spatial region r at t is to say that r is the spatial extent of s at t. (axiom label in BFO2 Reference: [081-003])