翻訳と辞書 Words near each other ・ Standard test tone ・ Standard Textile Company ・ Standard Thai Astrology Manual ・ Standard Theatre ・ Standard Theatre (Philadelphia) ・ Standard Theatre (Toronto) ・ Standard Tibetan ・ Standard time ・ Standard Time (album) ・ Standard time (manufacturing) ・ Standard Time Act ・ Standard time and frequency signal service ・ Standard time in manufacturing ・ Standard Tool & Manufacturing ・ Standard trading conditions ・ Standard translation ・ Standard Treasury ・ Standard treatment ・ Standard tuning ・ Standard units ・ Standard upper ontology ・ Standard Vacuum Oil Company ・ Standard Vanguard ・ Standard weight in fish ・ Standard wet liner inline-four engine ・ Standard Widget Toolkit ・ Standard wind tunnel models ・ Standard wire gauge ・ Standard works ・ Standard World Tv Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Standard translation ： ウィキペディア英語版 Standard translation In modal logic, standard translation is a way of transforming formulas of modal logic into formulas of first-order logic which capture the meaning of the modal formulas. Standard translation is defined inductively on the structure of the formula. In short, atomic formulas are mapped onto unary predicates and the objects in the first-order language are the accessible worlds. The logical connectives from propositional logic remain untouched and the modal operators are transformed into first-order formulas according to their semantics. == Definition == Standard translation is defined as follows: *$ST\_x(p)\; \backslash equiv\; P(x)$, where $p$ is an atomic formula; P(x) is true when $p$ holds in world $x$. *$ST\_x(\backslash top)\; \backslash equiv\; \backslash top$ *$ST\_x(\backslash bot)\; \backslash equiv\; \backslash bot$ *$ST\_x(\backslash neg\; \backslash varphi)\; \backslash equiv\; \backslash neg\; ST\_x(\backslash varphi)$ *$ST\_x(\backslash varphi\; \backslash wedge\; \backslash psi)\; \backslash equiv\; ST\_x(\backslash varphi)\; \backslash wedge\; ST\_x(\backslash psi)$ *$ST\_x(\backslash varphi\; \backslash vee\; \backslash psi)\; \backslash equiv\; ST\_x(\backslash varphi)\; \backslash vee\; ST\_x(\backslash psi)$ *$ST\_x(\backslash varphi\; \backslash rightarrow\; \backslash psi)\; \backslash equiv\; ST\_x(\backslash varphi)\; \backslash rightarrow\; ST\_x(\backslash psi)$ *$ST\_x(\backslash Diamond\_m\; \backslash varphi)\; \backslash equiv\; \backslash exists\; y\; (\; R\_m(x,\; y)\; \backslash wedge\; ST\_y(\backslash varphi))$ *$ST\_x(\backslash Box\_m\; \backslash varphi)\; \backslash equiv\; \backslash forall\; y\; (\; R\_m(x,\; y)\; \backslash rightarrow\; ST\_y(\backslash varphi))$ In the above, $x$ is the world from which the formula is evaluated. Initially, a free variable $x$ is used and whenever a modal operator needs to be translated, a fresh variable is introduced to indicate that the remainder of the formula needs to be evaluated from that world. Here, the subscript $m$ refers to the accessibility relation that should be used: normally, $\backslash Box$ and $\backslash Diamond$ refer to a relation $R$ of the Kripke model but more than one accessibility relation can exist (a multimodal logic) in which case subscripts are used. For example, $\backslash Box\_a$ and $\backslash Diamond\_a$ refer to an accessibility relation $R\_a$ and $\backslash Box\_b$ and $\backslash Diamond\_b$ to $R\_b$ in the model. Alternatively, it can also be placed inside the modal symbol. 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「Standard translation」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.