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Sigma KEE - exactCardinality

exactCardinality

appearance as argument number 1

(documentation exactCardinality EnglishLanguage "This relation expresses the number of values that a particular argument to a relation can have if all other values remain fixed.")	Media.kif 2066-2069
(domain exactCardinality 1 Relation)	Media.kif 2071-2071	The number 1 argument of exactCardinality is an instance of relation
(domain exactCardinality 2 Integer)	Media.kif 2072-2072	The number 2 argument of exactCardinality is an instance of integer
(domain exactCardinality 3 Integer)	Media.kif 2073-2073	The number 3 argument of exactCardinality is an instance of integer
(instance exactCardinality TernaryPredicate)	Media.kif 2070-2070	exactCardinality is an instance of ternary predicate

appearance as argument number 2

(format ChineseLanguage exactCardinality "那只能是 %3 values 对于 %1 的参数 %2 ")	domainEnglishFormat.kif 3335-3335
(format ChineseTraditionalLanguage exactCardinality "那只能是 %3 values 對於 %1 的參數 %2 ")	domainEnglishFormat.kif 3334-3334
(format EnglishLanguage exactCardinality "there can be %3 values to argument %2 of %1")	domainEnglishFormat.kif 3333-3333

antecedent

(=> (and (exactCardinality ?REL ?ARG 1) (instance ?REL Predicate) (?REL @ARGS) (equal ?X (ListOrderFn (ListFn @ARGS) ?ARG)) (equal ?Y (ListOrderFn (ListFn @ARGS) ?ARG))) (equal ?X ?Y))	Media.kif 2108-2115	If there can be 1 values to argument a positive integer of a relation and the relation is an instance of predicate and the relation @ARGS and another entity is equal to the positive integerth element of (@ARGS) and a fourth entity is equal to the positive integerth element of (@ARGS), then the other entity is equal to the fourth entity
(=> (and (exactCardinality ?REL ?ARG 1) (instance ?REL Predicate) (?REL @ARGS) (equal ?X (ListOrderFn (ListFn @ARGS) ?ARG))) (not (exists (?Y) (and (equal ?Y (ListOrderFn (ListFn @ARGS) ?ARG)) (not (equal ?X ?Y))))))	Media.kif 2095-2105	If there can be 1 values to argument a positive integer of a relation and the relation is an instance of predicate and the relation @ARGS and another entity is equal to the positive integerth element of (@ARGS), then there doesn't exist a fourth entity such that the fourth entity is equal to the positive integerth element of (@ARGS) and the other entity is not equal to the fourth entity
(=> (and (exactCardinality ?REL ?ARG 1) (instance ?REL Predicate)) (exists (?X @ARGS) (and (?REL @ARGS) (equal ?X (ListOrderFn (ListFn @ARGS) ?ARG)) (not (exists (?Y) (and (equal ?Y (ListOrderFn (ListFn @ARGS) ?ARG)) (not (equal ?X ?Y))))))))	Media.kif 2077-2092	If there can be 1 values to argument a positive integer of a relation and the relation is an instance of predicate, then there exist an entity and @ARGS such that the relation @ARGS and the entity is equal to the positive integerth element of (@ARGS) and there doesn't exist a fourth entity such that the fourth entity is equal to the positive integerth element of (@ARGS) and the entity is not equal to the fourth entity
(=> (and (exactCardinality ?REL ?ARG ?COUNT) (instance ?REL Predicate)) (exists (?S) (and (instance ?S SetOrClass) (=> (and (?REL @ARGS) (equal ?EL (ListOrderFn (ListFn @ARGS) ?ARG))) (and (instance ?EL ?S) (equal (CardinalityFn ?S) ?COUNT))))))	Media.kif 2134-2147	If there can be an integer values to argument a positive integer of a relation and the relation is an instance of predicate, then there exists a set or class such that the set or class is an instance of set or class and if the relation @ARGS and another entity is equal to the positive integerth element of (@ARGS), then the other entity is an instance of the set or class and the number of instances in the set or class is equal to the integer
(=> (exactCardinality ?REL ?ARG ?COUNT) (equal (CardinalityFn (KappaFn ?EL (and (?REL @ARGS) (equal ?EL (ListOrderFn (ListFn @ARGS) ?ARG))))) ?COUNT))	Media.kif 2123-2131	If there can be an integer values to argument another integer of a relation, then the number of instances in the class described by a symbolic string is equal to the integer

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