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Sigma KEE - BinaryRelation
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binary relation
BinaryRelations are relations that are true only of pairs of things. BinaryRelations are represented as slots in frame systems.
Relationships      
Parents inheritable relation The class of Relations whose properties can be inherited downward in the class hierarchy via the subrelation Predicate.
  relation The Class of relations. There are three kinds of Relation: Predicate, Function, and List. Predicates and Functions both denote sets of ordered n-tuples. The difference between these two Classes is that Predicates cover formula-forming operators, while Functions cover term-forming operators. A List, on the other hand, is a particular ordered n-tuple.
Children antisymmetric relationBinaryRelation ?REL is an AntisymmetricRelation if for distinct ?INST1 and ?INST2, (?REL ?INST1 ?INST2) implies not (?REL ?INST2 ?INST1). In other words, for all ?INST1 and ?INST2, (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST1) imply that ?INST1 and ?INST2 are identical. Note that it is possible for an AntisymmetricRelation to be a ReflexiveRelation.
 binary predicateA Predicate relating two items - its valence is two.
 economic relationA class of Relations which are used to specify various economic measures, e.g. the GDP, the consumer price index, and the trade deficit.
 intransitive relationA BinaryRelation ?REL is intransitive only if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply not (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3.
 irreflexive relationRelation ?REL is irreflexive iff (?REL ?INST ?INST) holds for no value of ?INST.
 reflexive relationRelation ?REL is reflexive iff (?REL ?INST ?INST) for all ?INST.
 symmetric relationA BinaryRelation ?REL is symmetric just iff (?REL ?INST1 ?INST2) imples (?REL ?INST2 ?INST1), for all ?INST1 and ?INST2.
 transitive relationA BinaryRelation ?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3.
 trichotomizing relationA BinaryRelation ?REL is a TrichotomizingRelation just in case all ordered pairs consisting of distinct individuals are elements of ?REL.
 unary functionThe Class of Functions that require a single argument.


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