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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 Turnstile (symbol) ： ウィキペディア英語版 Turnstile (symbol) In mathematical logic and computer science the symbol $\backslash vdash$ has taken the name turnstile because of its resemblance to a typical turnstile if viewed from above. It is also referred to as tee and is often read as "yields", "proves", "satisfies" or "entails". The symbol was first used by Gottlob Frege in his 1879 book on logic, ''Begriffsschrift''. Martin-Löf analyzes the $\backslash vdash$ symbol thus: "...()he combination of Frege's Urteilsstrich, judgement stroke (), and Inhaltsstrich, content stroke (), came to be called the assertion sign." Frege's notation for a judgement of some content $A$ :$\backslash vdash\; A$ can be then be read :''I know $A$ is true''". In the same vein, a conditional assertion :$P\; \backslash vdash\; Q$ can be read as: :''From $P$, I know that $Q$'' In TeX, the turnstile symbol $\backslash vdash$ is obtained from the command \vdash. In Unicode, the turnstile symbol ((unicode:⊢)) is called right tack and is at code point U+22A2.〔(Unicode standard )〕 On a typewriter, a turnstile can be composed from a vertical bar (|) and a dash (–). In LaTeX there is a turnstile package which issues this sign in many ways, and is capable of putting labels below or above it, in the correct places.〔http://www.ctan.org/tex-archive/macros/latex/contrib/turnstile〕 == Interpretations == The turnstile represents a binary relation. It has several different interpretations in different contexts: * In metalogic, the study of formal languages; the turnstile represents syntactic consequence (or "derivability"). This is to say, that it shows that one string can be derived from another in a single step, according to the transformation rules (i.e. the syntax) of some given formal system.〔http://dingo.sbs.arizona.edu/~hammond/ling178-sp06/mathCh6.pdf〕 As such, the expression :$P\; \backslash vdash\; Q$ :means that $Q$ is derivable from $P$ in the system. :Consistent with its use for derivability, a "$\backslash vdash$" followed by an expression without anything preceding it denotes a theorem, which is to say that the expression can be derived from the rules using an empty set of axioms. As such, the expression :$\backslash vdash\; Q$ :means that $Q$ is a theorem in the system. *In proof theory, the turnstile is used to denote "provability". For example, if $T$ is a formal theory and $S$ is a particular sentence in the language of the theory then :$T\; \backslash vdash\; S$ :means that $S$ is provable from $T$. This usage is demonstrated in the article on propositional calculus. * In the typed lambda calculus, the turnstile is used to separate typing assumptions from the typing judgment.〔http://www.mscs.dal.ca/~selinger/papers/lambdanotes.pdf〕 * In category theory, a reversed turnstile (⊣), as in $F\; \backslash dashv\; G$, is used to indicate that the functor $F$ is left adjoint to the functor $G$. * In APL the symbol is called "right tack" and represents the ambivalent right identity function where both ''X⊢Y'' and ''⊢Y'' are ''Y''. The reversed symbol "⊣" is called "left tack" and represents the analogous left identity where ''X⊣Y'' is ''X'' and ''⊣Y'' is ''Y''.〔http://www.jsoftware.com/papers/APLDictionary.htm〕 * In combinatorics, $\backslash lambda\; \backslash vdash\; n$ means that $\backslash lambda$ is a partition (number theory) of the integer $n$. 〔p.287 of Stanley, Richard P.. Enumerative Combinatorics. 1st ed. Vol. 2. Cambridge: Cambridge University Press, 1999. 〕 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「Turnstile (symbol)」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.