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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > PartialOrderingRelation

PartialOrderingRelation
subject			fact

PartialOrderingRelation	documentation A BinaryRelation is a partial ordering if it is a ReflexiveRelation, an AntisymmetricRelation, and a TransitiveRelation
	is a kind of AntisymmetricRelation
	is a kind of ReflexiveRelation
	is a kind of TransitiveRelation
AntisymmetricRelation	has axiom (=> (partialOrderingOn ?RELATION ?CLASS) (and (reflexiveOn ?RELATION ?CLASS) (instance ?RELATION TransitiveRelation) (instance ?RELATION AntisymmetricRelation)))
	has axiom (=> (instance ?REL AntisymmetricRelation) (forall (?INST1 ?INST2) (=> (and (holds ?REL ?INST1 ?INST2) (holds ?REL ?INST2 ?INST1)) (equal ?INST1 ?INST2))))
ReflexiveRelation	has axiom (=> (instance ?REL ReflexiveRelation) (forall (?INST) (holds ?REL ?INST ?INST)))
TransitiveRelation	has axiom (=> (partialOrderingOn ?RELATION ?CLASS) (and (reflexiveOn ?RELATION ?CLASS) (instance ?RELATION TransitiveRelation) (instance ?RELATION AntisymmetricRelation)))
	has axiom (=> (equivalenceRelationOn ?RELATION ?CLASS) (and (instance ?RELATION TransitiveRelation) (instance ?RELATION SymmetricRelation) (reflexiveOn ?RELATION ?CLASS)))
	has axiom (=> (instance ?REL TransitiveRelation) (forall (?INST1 ?INST2 ?INST3) (=> (and (holds ?REL ?INST1 ?INST2) (holds ?REL ?INST2 ?INST3)) (holds ?REL ?INST1 ?INST3))))
BinaryRelation	is first domain of DomainFn
	is first domain of equivalenceRelationOn
	is first domain of inverse
	is first domain of irreflexiveOn
	is first domain of partialOrderingOn
	is first domain of RangeFn
	is first domain of reflexiveOn
	is first domain of totalOrderingOn
	is first domain of trichotomizingOn
	is second domain of inverse
Class	is third domain of domain
	is third domain of domainSubclass
Abstract	is disjoint from Physical

Kinds of PartialOrderingRelation :

• beforeEq (5 facts) - (beforeEq ?POINT1 ?POINT2) means that ?POINT1 is identical with ?POINT2 or occurs before it on the universal timeline
• greaterThanOrEqualTo (11 facts) - (greaterThanOrEqualTo ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is greater than the Quantity ?NUMBER2
• lessThanOrEqualTo (10 facts) - (lessThanOrEqualTo ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is less than or equal to the Quantity ?NUMBER2
• located (18 facts) - A very general predicate. (located ?PHYS ?OBJ) means that ?PHYS is situated at ?OBJ, in some sense. The Predicates located and existant are spatial and temporal predicates, respectively
• overlapsTemporally (9 facts) - (overlapsTemporally ?INTERVAL1 ?INTERVAL2) means that the two TimeIntervals ?INTERVAL1 and ?INTERVAL2 have a TimeInterval in common. Note that this is consistent with ?INTERVAL1 and ?INTERVAL2 being the same TimeInterval
• part (51 facts) - The basic mereological relation. All other mereological relations are defined in terms of this one. (part ?PART ?WHOLE) simply means that the Object ?PART is part of the Object ?WHOLE. Note that, since part is a ReflexiveRelation, every Object is a part of itself
• subAttribute (6 facts) - Means that the second argument can be ascribed to everything which has the first argument ascribed to it
• subclass (22 facts) - Class C is a subclass of Class P only if every instance of C is also an instance of P. A class may have multiple superclasses and subclasses
• subProcess (18 facts) - (subProcess ?SUBPROC ?PROC) means that ?SUBPROC is a subprocess of ?PROC. A subprocess is here understood as a temporally distinguished part (proper or not) of a Process
• subrelation (11 facts) - A Relation R is a subrelation Relation R' if R is a subclass R'. This implies that every tuple of R is also a tuple of R'. Again, if R holds for some arguments arg_1, arg_2, ... arg_n, then R' holds for the same arguments. Thus, a Relation and its subrelation must have the same valence. In CycL, subrelation is called #$genlPreds
• subsumesContentClass (7 facts) - A BinaryPredicate that relates two subclasses of ContentBearingObject. (subsumesContentClass ?CLASS1 ?CLASS2) means that the content expressed by each instance of ?CLASS1 is also expressed by each instance of ?CLASS2. Examples include the relationship between a poem and one of its stanzas or between a book and one of its chapters. Note that this is a relation between subclasses of ContentBearingObject, rather than instances. If one wants to relate instances, the Predicate subsumesContentInstance can be used. Note that subsumesContentClass is needed in many cases. Consider, for example, the relation between the King James edition of the Bible and its Book of Genesis. This relation holds for every copy of this edition and not just for a single instance
• subsumesContentInstance (10 facts) - A BinaryPredicate relating two instances of ContentBearingObject. (subsumesContentInstance ?OBJ1 ?OBJ2) means that the content expressed by ?OBJ2 is part of the content expressed by ?OBJ1. An example is the relationship between a handwritten poem and one of its stanzas. Note that this is a relation between instances, rather than Classes. If one wants to assert a content relationship between Classes, e.g. between the version of an intellectual work and a part of that work, the relation subsumesContentClass should be used
• TotalOrderingRelation (4 facts) - "A BinaryRelation is a TotalOrderingRelation if it is a PartialOrderingRelation and a TrichotomizingRelation

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