| SymmetricRelation(symmetric relation) | | contrarily, contrariwise, on_the_contrary, the_other_way_around, to_the_contrary, vice_versa |
| appearance as argument number 1 |
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| (subclass SymmetricRelation BinaryRelation) | Merge.kif 2370-2370 | Symmetric relation is a subclass of binary relation |
| (disjoint SymmetricRelation AntisymmetricRelation) | Merge.kif 2371-2371 | Symmetric relation is disjoint from antisymmetric relation |
| (documentation SymmetricRelation EnglishLanguage "A BinaryRelation ?REL is symmetric just iff (?REL ?INST1 ?INST2) imples (?REL ?INST2 ?INST1), for all ?INST1 and ?INST2.") | Merge.kif 2373-2375 | Symmetric relation is disjoint from antisymmetric relation |
| appearance as argument number 2 |
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| antecedent |
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| (=> (instance ?REL SymmetricRelation) (forall (?INST1 ?INST2) (=> (?REL ?INST1 ?INST2) (?REL ?INST2 ?INST1)))) |
Merge.kif 2377-2382 | If X is an instance of symmetric relation, then For all Entities Y and Z: if X Y and Z, then X Z and Y |
| consequent |
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| (=> (equivalenceRelationOn ?RELATION ?CLASS) (and (instance ?RELATION TransitiveRelation) (instance ?RELATION SymmetricRelation) (reflexiveOn ?RELATION ?CLASS))) |
Merge.kif 3819-3824 | If X is an equivalence relation on Y, then X is an instance of transitive relation, X is an instance of symmetric relation, and X is reflexive on Y |
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