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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 Monadic predicate calculus ： ウィキペディア英語版 Monadic predicate calculus In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic in which all relation symbols in the signature are monadic (that is, they take only one argument), and there are no function symbols. All atomic formulas are thus of the form $P(x)$, where $P$ is a relation symbol and $x$ is a variable. Monadic predicate calculus can be contrasted with polyadic predicate calculus, which allows relation symbols that take two or more arguments. == Expressiveness == The absence of polyadic relation symbols severely restricts what can be expressed in the monadic predicate calculus. It is so weak that, unlike the full predicate calculus, it is decidable - there is a decision procedure that determines whether a given formula of monadic predicate calculus is logically valid (true for all nonempty domains).〔Heinrich Behmann, ''Beiträge zur Algebra der Logik, insbesondere zum Entscheidungsproblem'', in ''Mathematische Annalen'' (1922)〕〔Löwenheim, L. (1915) "Über Möglichkeiten im Relativkalkül," ''Mathematische Annalen'' 76: 447-470. Translated as "On possibilities in the calculus of relatives" in Jean van Heijenoort, 1967. ''A Source Book in Mathematical Logic'', 1879-1931. Harvard Univ. Press: 228-51.〕 Adding a single binary relation symbol to monadic logic, however, results in an undecidable logic. 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「Monadic predicate calculus」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.