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be second domain of |
be first domain of |
have axiom |
BinaryRelation | BinaryRelations map instances of a Class to instances of another Class. BinaryRelations are represented as slots in frame systems | inverse | trichotomizingOn | (=> (and (inverse ?REL1 ?REL2) (instance ?REL1 BinaryRelation) (instance ?REL2 BinaryRelation)) (forall (?INST1 ?INST2) (<=> (holds ?REL1 ?INST1 ?INST2) (holds ?REL2 ?INST2 ?INST1))))
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Function | A Function is a term-forming Relation that maps from a n-tuple of arguments to a range and that associates this n-tuple with exactly one range element. Note that the range is a Class, and each element of the range is an instance of the Class | subrelation | rangeSubclass | (forall (?INT) (domain exhaustiveDecomposition ?INT Class))
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Predicate | A Predicate is a sentence-forming Relation. Each tuple in the Relation is a finite, ordered sequence of objects. The fact that a particular tuple is an element of a Predicate is denoted by '(*predicate* arg_1 arg_2 .. arg_n)', where the arg_i are the objects so related. In the case of BinaryPredicates, the fact can be read as `arg_1 is *predicate* arg_2' or `a *predicate* of arg_1 is arg_2' | subrelation | singleValued | (forall (?INT) (domain exhaustiveDecomposition ?INT Class))
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ProbabilityRelation | The Class of Relations that permit assessment of the probability of an event or situation | subrelation | valence | (forall (?INT) (domain exhaustiveDecomposition ?INT Class))
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QuaternaryRelation | QuaternaryRelations relate four items. The two subclasses of QuaternaryRelation are QuaternaryPredicate and TernaryFunction | subrelation | valence | (forall (?INT) (domain exhaustiveDecomposition ?INT Class))
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QuintaryRelation | QuintaryRelations relate five items. The two subclasses of QuintaryRelation are QuintaryPredicate and QuaternaryFunction | subrelation | valence | (forall (?INT) (domain exhaustiveDecomposition ?INT Class))
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RelationExtendedToQuantities | A RelationExtendedToQuantities is a Relation that, when it is true on a sequence of arguments that are RealNumbers, it is also true on a sequence of ConstantQuantites with those magnitudes in some unit of measure. For example, the lessThan relation is extended to quantities. This means that for all pairs of quantities ?QUANTITY1 and ?QUANTITY2, (lessThan ?QUANTITY1 ?QUANTITY2) if and only if, for some ?NUMBER1, ?NUMBER2, and ?UNIT, ?QUANTITY1 = (MeasureFn ?NUMBER1 ?UNIT), ?QUANTITY2 = (MeasureFn ?NUMBER2 ?UNIT), and (lessThan ?NUMBER1 ?NUMBER2), for all units ?UNIT on which ?QUANTITY1 and ?QUANTITY2 can be measured. Note that, when a RelationExtendedToQuantities is extended from RealNumbers to ConstantQuantities, the ConstantQuantities must be measured along the same physical dimension | subrelation | valence | (=> (and (instance ?REL RelationExtendedToQuantities) (instance ?REL BinaryRelation) (instance ?NUMBER1 RealNumber) (instance ?NUMBER2 RealNumber) (holds ?REL ?NUMBER1 ?NUMBER2)) (forall (?UNIT) (=> (instance ?UNIT UnitOfMeasure) (holds ?REL (MeasureFn ?NUMBER1 ?UNIT) (MeasureFn ?NUMBER2 ?UNIT)))))
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SpatialRelation | The Class of Relations that are spatial in a wide sense. This Class includes mereological relations, topological relations, and positional relations | subrelation | valence | (=> (and (instance ?REL SpatialRelation) (holds ?REL ?OBJ1 ?OBJ2)) (overlapsTemporally (WhenFn ?OBJ1) (WhenFn ?OBJ2)))
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TemporalRelation | The Class of temporal Relations. This Class includes notions of (temporal) topology of intervals, (temporal) schemata, and (temporal) extension | subrelation | valence | (forall (?INT) (domain exhaustiveDecomposition ?INT Class))
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TernaryRelation | TernaryRelations relate three items. The two subclasses of TernaryRelation are TernaryPredicate and BinaryFunction | subrelation | valence | (forall (?INT) (domain exhaustiveDecomposition ?INT Class))
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VariableArityRelation | The Class of Relations that do not have a fixed number of arguments | subrelation | valence | (=> (instance ?REL VariableArityRelation) (not (exists (?INT) (valence ?REL ?INT))))
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