Relation Comparison Table

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Relation comparison table

Subject documentation 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))))

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))

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))

ProbabilityRelation The Class of Relations that permit assessment of the probability of an event or situation subrelation valence
(forall (?INT) (domain exhaustiveDecomposition ?INT Class))

QuaternaryRelation QuaternaryRelations relate four items. The two subclasses of QuaternaryRelation are QuaternaryPredicate and TernaryFunction subrelation valence
(forall (?INT) (domain exhaustiveDecomposition ?INT Class))

QuintaryRelation QuintaryRelations relate five items. The two subclasses of QuintaryRelation are QuintaryPredicate and QuaternaryFunction subrelation valence
(forall (?INT) (domain exhaustiveDecomposition ?INT Class))

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)))))

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)))

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))

TernaryRelation TernaryRelations relate three items. The two subclasses of TernaryRelation are TernaryPredicate and BinaryFunction subrelation valence
(forall (?INT) (domain exhaustiveDecomposition ?INT Class))

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))))

Subject	documentation	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))))
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))
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))
ProbabilityRelation	The Class of Relations that permit assessment of the probability of an event or situation	subrelation	valence	(forall (?INT) (domain exhaustiveDecomposition ?INT Class))
QuaternaryRelation	QuaternaryRelations relate four items. The two subclasses of QuaternaryRelation are QuaternaryPredicate and TernaryFunction	subrelation	valence	(forall (?INT) (domain exhaustiveDecomposition ?INT Class))
QuintaryRelation	QuintaryRelations relate five items. The two subclasses of QuintaryRelation are QuintaryPredicate and QuaternaryFunction	subrelation	valence	(forall (?INT) (domain exhaustiveDecomposition ?INT Class))
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)))))
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)))
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))
TernaryRelation	TernaryRelations relate three items. The two subclasses of TernaryRelation are TernaryPredicate and BinaryFunction	subrelation	valence	(forall (?INT) (domain exhaustiveDecomposition ?INT Class))
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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