PairwiseDisjointClass Comparison Table

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PairwiseDisjointClass comparison table

Subject documentation is a kind of have axiom

Class Class generalizes Set. Classes, like Sets, are collections of things. Accordingly, the notion of membership is generalized as well - a member of a Class is an instance the Class. Classes can differ from Sets in two important respects. First, Classes that are not explicitly identified as Sets are not assumed to be extensional. That is, distinct Classes might well have exactly the same instances. Second, Classes typically have an associated `condition' that determines the instances of the Class. So, for example, the condition `human' determines the Class of Humans. Note that some Classes might satisfy their own condition (e.g., the Class of Abstract things is Abstract) and hence be instances of themselves Abstract
(forall (?INT) (domain exhaustiveDecomposition ?INT Class))

PairwiseDisjointClass A Class of Classes is a PairwiseDisjointClass just in case every instance of the Class is either equal to or disjoint from every other instance of the Class Class
(=>
(instance ?SUPERCLASS PairwiseDisjointClass)
(forall (?CLASS1 ?CLASS2)
(=>
(and
(instance ?CLASS1 ?SUPERCLASS)
(instance ?CLASS2 ?SUPERCLASS))
(or
(equal ?CLASS1 ?CLASS2)
(disjoint ?CLASS1 ?CLASS2)))))

Subject	documentation	is a kind of	have axiom
Class	Class generalizes Set. Classes, like Sets, are collections of things. Accordingly, the notion of membership is generalized as well - a member of a Class is an instance the Class. Classes can differ from Sets in two important respects. First, Classes that are not explicitly identified as Sets are not assumed to be extensional. That is, distinct Classes might well have exactly the same instances. Second, Classes typically have an associated `condition' that determines the instances of the Class. So, for example, the condition `human' determines the Class of Humans. Note that some Classes might satisfy their own condition (e.g., the Class of Abstract things is Abstract) and hence be instances of themselves	Abstract	(forall (?INT) (domain exhaustiveDecomposition ?INT Class))
PairwiseDisjointClass	A Class of Classes is a PairwiseDisjointClass just in case every instance of the Class is either equal to or disjoint from every other instance of the Class	Class	(=> (instance ?SUPERCLASS PairwiseDisjointClass) (forall (?CLASS1 ?CLASS2) (=> (and (instance ?CLASS1 ?SUPERCLASS) (instance ?CLASS2 ?SUPERCLASS)) (or (equal ?CLASS1 ?CLASS2) (disjoint ?CLASS1 ?CLASS2)))))

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