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Entity > Abstract > Class > Relation > BinaryRelation > TransitiveRelation

TransitiveRelation
subject			fact

TransitiveRelation	documentation A BinaryRelation ?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3
	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))))
	is a kind of BinaryRelation
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 TransitiveRelation :

• above (6 facts) - This is a cognitive primitive, derived from the up/down schema and not involving contact. (above ?OBJ1 ?OBJ2) means that ?OBJ1 is above ?OBJ2
• before (6 facts) - (before ?POINT1 ?POINT2) means that ?POINT1 precedes ?POINT2 on the universal timeline
• behind (3 facts) - This is a cognitive primitive, derived from the front/back schema. (behind ?OBJ1 ?OBJ2) means that ?OBJ1 is behind ?OBJ2
• below (4 facts) - This is a cognitive primitive, derived from the up/down schema and not involving contact. (below ?OBJ1 ?OBJ2) means that ?OBJ1 is below ?OBJ2
• contains (4 facts) - Limits, bounds, confines, encloses or circumscribes - the surrounding relation for Objects. (contains ?OBJ1 ?OBJ2) means that the interior of ?OBJ1 wholly surrounds ?OBJ2
• contraryProperty (8 facts) - Means that the two arguments are properties that are opposed to one another, e.g. Pliable versus Rigid
• crosses (5 facts) - (crosses ?OBJ1 ?OBJ2) means that Object ?OBJ1 traverses Object ?OBJ2, without being connected to it
• developmentalForm (8 facts) - (developmentalForm ?OBJECT ?FORM) means that ?FORM is an earlier stage in the individual maturation of ?OBJECT. For example, tadpole and caterpillar are developmentalForms of frogs and butterflies, respectively
• during (9 facts) - (during ?INTERVAL1 ?INTERVAL2) means that ?INTERVAL1 starts after and ends before ?INTERVAL2
• earlier (8 facts) - (earlier INTERVAL1 INTERVAL2) means that INTERVAL1 ends before INTERVAL2 begins
• EquivalenceRelation (10 kinds, 59 facts) - A BinaryRelation is an equivalence relation if it is a ReflexiveRelation, a SymmetricRelation, and a TransitiveRelation
• finishes (7 facts) - (finishes ?INTERVAL1 ?INTERVAL2) means that ?INTERVAL1 and ?INTERVAL2 are both TimeIntervals that have the same ending TimePoint and that ?INTERVAL2 begins before ?INTERVAL1
• front (4 facts) - This is a cognitive primitive, derived from the front/back schema. (front ?OBJ1 ?OBJ2) means that ?OBJ1 is in front of ?OBJ2
• greaterThan (16 facts) - (greaterThan ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is greater than the Quantity ?NUMBER2
• larger (8 facts) - (larger ?OBJ1 ?OBJ2) simply means that ?OBJ1 is larger, with respect to all LengthMeasures, than ?OBJ2
• left (4 facts) - This is a cognitive primitive, derived from the left/right schema. (left ?OBJ1 ?OBJ2) means that ?OBJ1 is to the left ?OBJ2
• lessThan (20 facts) - (lessThan ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is less than the Quantity ?NUMBER2
• PartialOrderingRelation (13 kinds, 186 facts) - A BinaryRelation is a partial ordering if it is a ReflexiveRelation, an AntisymmetricRelation, and a TransitiveRelation
• precondition (6 facts) - A very general Predicate. (precondition ?PROC1 ?PROC2) means that ?PROC2 can exist or be true only if ?PROC1 exists or is true. At some point, this Predicate should probably be broken up into more specific Predicates with more restrictive domain restrictions
• properPart (9 facts) - (properPart ?OBJ1 ?OBJ2) means that ?OBJ1 is a part of ?OBJ2 other than ?OBJ2 itself. This is a TransitiveRelation and AsymmetricRelation (hence an IrreflexiveRelation)
• right (4 facts) - This is a cognitive primitive, derived from the left/right schema. (right ?OBJ1 ?OBJ2) means that ?OBJ1 is to the right ?OBJ2
• smaller (8 facts) - (smaller ?OBJ1 ?OBJ2) simply means that ?OBJ1 is smaller, with respect to all LengthMeasures, than ?OBJ2
• starts (7 facts) - (starts ?INTERVAL1 ?INTERVAL2) means that ?INTERVAL1 and ?INTERVAL2 are both TimeIntervals that have the same initial TimePoint and that ?INTERVAL1 ends before ?INTERVAL2
• subCollection (6 facts) - (subCollection ?COLL1 ?COLL2) means that the Collection ?COLL1 is a proper part of the Collection ?COLL2
• subPlan (7 facts) - (subPlan ?PLAN1 ?PLAN2) means that ?PLAN1 is a Plan which is a proper part of ?PLAN2. This relation is generally used to relate a supporting Plan to the overall Plan in a particular context
• successorAttributeClosure (8 facts) - The transitive closure of successorAttribute. (successorAttributeClosure ?ATTR1 ?ATTR2) means that there is a chain of successorAttribute assertions connecting ?ATTR1 and ?ATTR2
• under (4 facts) - This is a cognitive primitive, derived from the up/down schema. (under ?OBJ1 ?OBJ2) means that ?OBJ1 is under ?OBJ2
• version (7 facts) - Some Artifacts have a life cycle with discrete stages or versions. (version ARTIFACT1 ARTIFACT2) means that ARTIFACT1 is a version of ARTIFACT2. Note that this Predicate relates subclasses of Artifact and not instances

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