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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Lindström quantifier ： ウィキペディア英語版 Lindström quantifier In mathematical logic, a Lindström quantifier is a generalized polyadic quantifier. They are a generalization of first-order quantifiers, such as the existential quantifier, the universal quantifier, and the counting quantifiers. They were introduced by Per Lindström in 1966. They were later studied for their applications in logic in computer science and database query languages. ==Generalization of first-order quantifiers== In order to facilitate discussion, some notational conventions need explaining. The expression : $\backslash phi^"\; TITLE="x,\backslash bar">)\backslash \}$ for ''A'' an ''L''-structure (or ''L''-model) in a language ''L'',''φ'' an ''L''-formula, and $\backslash bar$ a tuple of elements of the domain dom(''A'') of ''A''. In other words, $\backslash phi^$ of free variables, $\backslash phi^\}$ denotes an ''n''-ary relation defined on dom(''A''). Each quantifier $Q\_A$ is relativized to a structure, since each quantifier is viewed as a family of relations (between relations) on that structure. For a concrete example, take the universal and existential quantifiers ∀ and ∃, respectively. Their truth conditions can be specified as : $A\backslash models\backslash forall\; x\backslash phi()\; \backslash iff\; \backslash phi^"\; TITLE="x,\backslash bar">)\; \backslash iff\; \backslash phi^\},\backslash psi^\})\backslash in\; Q\_A$ where : $\backslash phi^\}=\backslash "\; TITLE="\backslash bar,\backslash bar">)\backslash \}$ for an ''n''-tuple $\backslash bar$ of variables. Lindström quantifiers are classified according to the number structure of their parameters. For example $Qxy\backslash phi(x)\backslash psi(y)$ is a type (1,1) quantifier, whereas $Qxy\backslash phi(x,y)$ is a type (2) quantifier. An example of type (1,1) quantifier is Hartig's quantifier testing equicardinality, i.e. the extension of . An example of a type (4) quantifier is the Henkin quantifier. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lindström quantifier」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.