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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 2011-2014
(instance exactCardinality TernaryPredicate) Media.kif 2015-2015 exact cardinality is an instance of ternary predicate
(domain exactCardinality 1 Relation) Media.kif 2016-2016 The number 1 argument of exact cardinality is an instance of relation
(domain exactCardinality 2 Integer) Media.kif 2017-2017 The number 2 argument of exact cardinality is an instance of integer
(domain exactCardinality 3 Integer) Media.kif 2018-2018 The number 3 argument of exact cardinality is an instance of integer

appearance as argument number 2
-------------------------


(format EnglishLanguage exactCardinality "there can be %3 values to argument %2 of %1") domainEnglishFormat.kif 3330-3330
(format ChineseTraditionalLanguage exactCardinality "那只能是 %3 values 對於 %1 的參數 %2 ") domainEnglishFormat.kif 3331-3331
(format ChineseLanguage exactCardinality "那只能是 %3 values 对于 %1 的参数 %2 ") domainEnglishFormat.kif 3332-3332
(termFormat EnglishLanguage exactCardinality "exact cardinality") domainEnglishFormat.kif 65836-65836

antecedent
-------------------------


(=>
    (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 2022-2037 If there can be 1 values to argument X of Y and Y is an instance of predicate, then there exist Z and @ARGS such that Y @ARGS and equal Z and V element of (@ARGS) and there doesn't exist U such that equal U and V element of (@ARGS) and equal Z and U
(=>
    (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 2040-2050 If there can be 1 values to argument X of Y, Y is an instance of predicate, Y @ARGS, and equal W and V element of (@ARGS), then there doesn't exist U such that equal U and V element of (@ARGS) and equal W and U
(=>
    (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 2053-2060 If there can be 1 values to argument X of Y, Y is an instance of predicate, Y @ARGS, equal W and V element of (@ARGS), and equal U and V element of (@ARGS), then equal W and U
(=>
    (exactCardinality ?REL ?ARG ?COUNT)
    (exists (?EL @ARGS)
        (equal
            (CardinalityFn
                (KappaFn ?EL
                    (and
                        (?REL @ARGS)
                        (equal ?EL
                            (ListOrderFn
                                (ListFn @ARGS) ?ARG))))) ?COUNT)))
Media.kif 2072-2081 If there can be X values to argument Y of Z, then there exist W, @ARGS such that equal the number of instances in the class described by W, and X
(=>
    (and
        (exactCardinality ?REL ?ARG ?COUNT)
        (instance ?REL Predicate))
    (exists (?S ?EL @ARGS)
        (and
            (instance ?S SetOrClass)
            (=>
                (and
                    (?REL @ARGS)
                    (equal ?EL
                        (ListOrderFn
                            (ListFn @ARGS) ?ARG)))
                (and
                    (instance ?EL ?S)
                    (equal
                        (CardinalityFn ?S) ?COUNT))))))
Media.kif 2084-2097 If there can be X values to argument Y of Z and Z is an instance of predicate, then there exist W, V and @ARGS such that W is an instance of set or class and Z @ARGS and equal V and T element of (@ARGS)V is an instance of W and equal the number of instances in W and X


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