VariableArityRelation Comparison Table

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VariableArityRelation comparison table

Subject have domain1 be first domain of have range documentation have axiom have relatedInternalConcept

AssignmentFn Function rangeSubclass Entity If F is a function with a value for the objects denoted by N1,..., NK, then the term (AssignmentFn F N1 ... NK) denotes the value of applying F to the objects denoted by N1,..., NK. Otherwise, the value is undefined
(=>
(instance ?FUNCTION CommutativeFunction)
(forall (?INST1 ?INST2)
(=>
(and
(instance ?INST1 (DomainFn ?FUNCTION))
(instance ?INST2 (DomainFn ?FUNCTION)))
(equal (AssignmentFn ?FUNCTION ?INST1 ?INST2)
(AssignmentFn ?FUNCTION ?INST2 ?INST1)))))

disjointDecomposition Class singleValued A disjointDecomposition of a Class C is a set of subclasses of C that are mutually disjoint
(forall (?INT) (domain disjointDecomposition ?INT Class))
exhaustiveDecomposition

exhaustiveDecomposition Class singleValued An exhaustiveDecomposition of a Class C is a set of subclasses of C such that every subclass of C either is an element of the set or is a subclass of an element of the set. Note: this does not necessarily mean that the elements of the set are disjoint (see partition - a partition is a disjoint exhaustive decomposition.
(forall (?INT) (domain exhaustiveDecomposition ?INT Class))
partition

GreatestCommonDivisorFn rangeSubclass Integer (GreatestCommonDivisorFn ?NUMBER1 ?NUMBER2 ... ?NUMBER) returns the greatest common divisor of ?NUMBER1 through ?NUMBER
(=>
(instance ?REL VariableArityRelation)
(not
(exists (?INT)
(valence ?REL ?INT))))

holds Relation singleValued (holds P N1 ... NK) is true just in case the tuple of objects denoted by N1,..., NK is an element of the Relation P
(=>
(instance ?REL VariableArityRelation)
(not
(exists (?INT)
(valence ?REL ?INT))))

LeastCommonMultipleFn rangeSubclass Integer (LeastCommonMultipleFn ?NUMBER1 ?NUMBER2 ... ?NUMBER) returns the least common multiple of ?NUMBER1 through ?NUMBER
(=>
(instance ?REL VariableArityRelation)
(not
(exists (?INT)
(valence ?REL ?INT))))

Subject	have domain1	be first domain of	have range	documentation	have axiom	have relatedInternalConcept
AssignmentFn	Function	rangeSubclass	Entity	If F is a function with a value for the objects denoted by N1,..., NK, then the term (AssignmentFn F N1 ... NK) denotes the value of applying F to the objects denoted by N1,..., NK. Otherwise, the value is undefined	(=> (instance ?FUNCTION CommutativeFunction) (forall (?INST1 ?INST2) (=> (and (instance ?INST1 (DomainFn ?FUNCTION)) (instance ?INST2 (DomainFn ?FUNCTION))) (equal (AssignmentFn ?FUNCTION ?INST1 ?INST2) (AssignmentFn ?FUNCTION ?INST2 ?INST1)))))
disjointDecomposition	Class	singleValued		A disjointDecomposition of a Class C is a set of subclasses of C that are mutually disjoint	(forall (?INT) (domain disjointDecomposition ?INT Class))	exhaustiveDecomposition
exhaustiveDecomposition	Class	singleValued		An exhaustiveDecomposition of a Class C is a set of subclasses of C such that every subclass of C either is an element of the set or is a subclass of an element of the set. Note: this does not necessarily mean that the elements of the set are disjoint (see partition - a partition is a disjoint exhaustive decomposition.	(forall (?INT) (domain exhaustiveDecomposition ?INT Class))	partition
GreatestCommonDivisorFn		rangeSubclass	Integer	(GreatestCommonDivisorFn ?NUMBER1 ?NUMBER2 ... ?NUMBER) returns the greatest common divisor of ?NUMBER1 through ?NUMBER	(=> (instance ?REL VariableArityRelation) (not (exists (?INT) (valence ?REL ?INT))))
holds	Relation	singleValued		(holds P N1 ... NK) is true just in case the tuple of objects denoted by N1,..., NK is an element of the Relation P	(=> (instance ?REL VariableArityRelation) (not (exists (?INT) (valence ?REL ?INT))))
LeastCommonMultipleFn		rangeSubclass	Integer	(LeastCommonMultipleFn ?NUMBER1 ?NUMBER2 ... ?NUMBER) returns the least common multiple of ?NUMBER1 through ?NUMBER	(=> (instance ?REL VariableArityRelation) (not (exists (?INT) (valence ?REL ?INT))))

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