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Entity > Abstract > Class > Relation > BinaryRelation > ReflexiveRelation > EquivalenceRelation

EquivalenceRelation
subject			fact

EquivalenceRelation	documentation A BinaryRelation is an equivalence relation if it is a ReflexiveRelation, a SymmetricRelation, and a TransitiveRelation
	is a kind of ReflexiveRelation
	is a kind of SymmetricRelation
	is a kind of TransitiveRelation
ReflexiveRelation	has axiom (=> (instance ?REL ReflexiveRelation) (forall (?INST) (holds ?REL ?INST ?INST)))
SymmetricRelation	has axiom (=> (equivalenceRelationOn ?RELATION ?CLASS) (and (instance ?RELATION TransitiveRelation) (instance ?RELATION SymmetricRelation) (reflexiveOn ?RELATION ?CLASS)))
	has axiom (=> (instance ?REL SymmetricRelation) (forall (?INST1 ?INST2) (=> (holds ?REL ?INST1 ?INST2) (holds ?REL ?INST2 ?INST2))))
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 EquivalenceRelation :

• adjacent (3 facts) - (adjacent ?OBJ1 ?OBJ2) means that ?OBJ1 is close to, near or abutting ?OBJ2 with no other structure of the same kind intervening. This Predicate covers the following relations: adjoins, abuts, is contiguous to, is juxtaposed, and is close to
• along (5 facts) - (along ?OBJ1 ?OBJ2) means that the Object ?OBJ1 shares the area of ?OBJ2 at least as far the extension of one dimension is concerned
• cooccur (7 facts) - (cooccur ?THING1 ?THING2) means that the Object or Process ?THING1 occurs at the same time as, together with, or jointly with the Object or Process ?THING2. This covers the following temporal relations: is co-incident with, is concurrent with, is contemporaneous with, and is concomitant with
• copy (6 facts) - relates an Object to an exact copy of the Object, where an exact copy is indistinguishable from the original with regard to every property except (possibly) spatial and/or temporal location
• equal (6 facts) - (equal ?ENTITY1 ?ENTITY2) is true just in case ?ENTITY1 is identical with ?ENTITY2
• equivalentContentClass (5 facts) - A BinaryPredicate that relates two subclasses of ContentBearingObject. (equivalentContentClass ?CLASS1 ?CLASS2) means that the content expressed by each instance of ?CLASS1 is also expressed by each instance of ?CLASS2, and vice versa. An example would be the relationship between English and Russian editions of Agatha Christie's 'Murder on the Orient Express'. Note that (equivalentContentClass ?CLASS1 ?CLASS2) implies (subsumesContentClass ?CLASS1 ?CLASS2) and (subsumesContentClass ?CLASS2 ?CLASS1)
• equivalentContentInstance (7 facts) - A BinaryPredicate relating two instances of ContentBearingObject. (equivalentContentInstance ?OBJ1 ?OBJ2) means that the content expressed by ?OBJ1 is identical to the content expressed by ?OBJ2. An example would be the relationship between a handwritten draft of a letter to one's lawyer and a typed copy of the same letter. Note that (equivalentContentInstance ?OBJ1 ?OBJ2) implies (subsumesContentInstance ?OBJ1 ?OBJ2) and (subsumesContentInstance ?OBJ2 ?OBJ2)
• familyRelation (7 facts) - A very general Predicate for biological relationships. (familyRelation ?ORGANISM1 ?ORGANISM2) means that ?ORGANISM1 and ?ORGANISM2 are biologically derived from a common ancestor
• near (4 facts) - The relation of common sense adjacency without contact. (near ?OBJ1 ?OBJ2) means that ?OBJ1 is near ?OBJ2
• relatedInternalConcept (5 facts) - Means that the two arguments are related concepts within the SUMO, i.e. there is a significant similarity of meaning between them. To indicate a meaning relation between a SUMO concept and a concept from another source, use the Predicate relatedExternalConcept

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