AssociativeFunction concept from the SUMO knowledge base

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AssociativeFunction

subject fact

AssociativeFunction documentation A BinaryFunction is associative if bracketing has no effect on the value returned by the Function. More precisely, a Function ?FUNCTION is associative just in case (?FUNCTION ?INST1 (?FUNCTION ?INST2 ?INST3)) is equal to (?FUNCTION (?FUNCTION ?INST1 ?INST2) ?INST3), for all ?INST1, ?INST2, and ?INST3 2001-11-30 13:33:39.0
has axiom
(=>
(instance ?FUNCTION AssociativeFunction)
(forall (?INST1 ?INST2 ?INST3)
(=>
(and
(instance ?INST1 (DomainFn ?FUNCTION))
(instance ?INST2 (DomainFn ?FUNCTION))
(instance ?INST3 (DomainFn ?FUNCTION)))
(equal (AssignmentFn ?FUNCTION ?INST1 (AssignmentFn ?FUNCTION ?INST1 ?INST2))
(AssignmentFn ?FUNCTION (AssignmentFn ?FUNCTION ?INST1 ?INST2) ?INST3)))))
2001-11-30 13:33:39.0
is a kind of BinaryFunction

BinaryFunction is first domain of distributes 2001-11-30 13:33:43.0
is first domain of identityElement
is second domain of distributes

Class is third domain of domain 2001-11-30 13:33:51.0
is third domain of domainSubclass

Abstract is disjoint from Physical 2001-11-30 13:33:32.0

Kinds of AssociativeFunction :

AdditionFn (9 facts) - If ?NUMBER1 and ?NUMBER2 are Numbers, then (AdditionFn ?NUMBER1 ?NUMBER2) is the arithmetical sum of these numbers
DivisionFn (15 facts) - If ?NUMBER1 and ?NUMBER2 are Numbers, then (DivisionFn ?NUMBER1 ?NUMBER2) is the result of dividing ?NUMBER1 by ?NUMBER2. An exception occurs when ?NUMBER1 = 1, in which case (DivisionFn ?NUMBER1 ?NUMBER2) is the reciprocal of ?NUMBER2
MaxFn (8 facts) - (MaxFn ?NUMBER1 ?NUMBER2) is the largest of ?NUMBER1 and ?NUMBER2. In cases where ?NUMBER1 is equal to ?NUMBER2, MaxFn returns one of its arguments
MinFn (8 facts) - (MinFn ?NUMBER1 ?NUMBER2) is the smallest of ?NUMBER1 and ?NUMBER2. In cases where ?NUMBER1 is equal to ?NUMBER2, MinFn returns one of its arguments
MultiplicationFn (52 facts) - If ?NUMBER1 and ?NUMBER2 are Numbers, then (MultiplicationFn ?NUMBER1 ?NUMBER2) is the arithmetical product of these numbers
SubtractionFn (10 facts) - If ?NUMBER1 and ?NUMBER2 are Numbers, then (SubtractionFn ?NUMBER1 ?NUMBER2) is the arithmetical difference between ?NUMBER1 and ?NUMBER2, i.e. ?NUMBER1 minus ?NUMBER2. An exception occurs when ?NUMBER1 is equal to 0, in which case (SubtractionFn ?NUMBER1 ?NUMBER2) is the negation of ?NUMBER2

AssociativeFunction	*documentation* A BinaryFunction is associative if bracketing has no effect on the value returned by the Function. More precisely, a Function ?FUNCTION is associative just in case (?FUNCTION ?INST1 (?FUNCTION ?INST2 ?INST3)) is equal to (?FUNCTION (?FUNCTION ?INST1 ?INST2) ?INST3), for all ?INST1, ?INST2, and ?INST3
	has axiom (=> (instance ?FUNCTION AssociativeFunction) (forall (?INST1 ?INST2 ?INST3) (=> (and (instance ?INST1 (DomainFn ?FUNCTION)) (instance ?INST2 (DomainFn ?FUNCTION)) (instance ?INST3 (DomainFn ?FUNCTION))) (equal (AssignmentFn ?FUNCTION ?INST1 (AssignmentFn ?FUNCTION ?INST1 ?INST2)) (AssignmentFn ?FUNCTION (AssignmentFn ?FUNCTION ?INST1 ?INST2) ?INST3)))))
	is a kind of BinaryFunction
BinaryFunction	*is first domain* of** distributes
	*is first domain* of** identityElement
	*is second domain* of** distributes
Class	*is third domain* of** domain
Class	*is third domain* of** domainSubclass
Abstract	*is disjoint* from** Physical