part of continuant at some time (forall (x y t) (if (and (continuantPartOfAt x y t) (IndependentContinuant x)) (locatedInAt x y t))) // axiom label in BFO2 CLIF: [047-002] [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) BFO2 Reference: continuantThe range for ‘t’ (as in all cases throughout this document unless otherwise specified) is: temporal region. [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]) (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] (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 t) (if (Continuant x) (continuantPartOfAt x x t))) // axiom label in BFO2 CLIF: [111-002] (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 y z t) (if (and (continuantPartOfAt x y t) (continuantPartOfAt y z t)) (continuantPartOfAt x z t))) // axiom label in BFO2 CLIF: [110-001] 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. BFO2 Reference: continuant Mary’s arm continuant_part_of Mary in the time of her life prior to her operation c-part-of_st (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] continuantPartOfAt 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 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. has continuant part at some time continuant continuant