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Relationships
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InheritableRelation |
The class of Relations whose properties can be inherited downward in the class hierarchy via the subrelation Predicate.
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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.
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AntisymmetricRelation | BinaryRelation ?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. |
| | BinaryPredicate | A Predicate relating two items - its valence is two. |
| | EconomicRelation | A class of Relations which are used to specify various economic measures, e.g. the GDP, the consumer price index, and the trade deficit. |
| | IntransitiveRelation | A BinaryRelation ?REL is intransitive only if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply not (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3. |
| | IrreflexiveRelation | Relation ?REL is irreflexive iff (?REL ?INST ?INST) holds for no value of ?INST. |
| | ReflexiveRelation | Relation ?REL is reflexive iff (?REL ?INST ?INST) for all ?INST. |
| | SymmetricRelation | A BinaryRelation ?REL is symmetric just iff (?REL ?INST1 ?INST2) imples (?REL ?INST2 ?INST1), for all ?INST1 and ?INST2. |
| | TransitiveRelation | A BinaryRelation ?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3. |
| | TrichotomizingRelation | A BinaryRelation ?REL is a TrichotomizingRelation just in case all ordered pairs consisting of distinct individuals are elements of ?REL. |
| | UnaryFunction | The Class of Functions that require a single argument. |