part of continuant at some time part of continuant at all times (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] BFO2 Reference: continuant (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] continuantPartOfAt [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) c-part-of_at 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] 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 (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 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]) Mary’s arm continuant_part_of Mary in the time of her life prior to her operation [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' 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. 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 all times that part exists