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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 Pregroup grammar ： ウィキペディア英語版 Pregroup grammar Pregroup grammar (PG) is a grammar formalism intimately related to categorial grammars. Much like categorial grammar (CG), PG is a kind of type logical grammar. Unlike CG, however, PG does not have a distinguished function type. Rather, PG uses inverse types combined with its monoidal operation. == Definition of a pregroup == A pregroup is a partially ordered algebra $(A,\; 1,\; \backslash cdot,\; -^l,\; -^r,\; \backslash leq)$ such that $(A,\; 1,\; \backslash cdot)$ is a monoid, satisfying the following relations: * $x^l\; \backslash cdot\; x\; \backslash leq\; 1\; \backslash qquad\; x\; \backslash cdot\; x^r\; \backslash leq\; 1$     (contraction) * $1\; \backslash leq\; x\; \backslash cdot\; x^l\; \backslash qquad\; 1\; \backslash leq\; x^r\; \backslash cdot\; x$     (expansion) The contraction and expansion relations are sometimes called Ajdukiewicz laws. From this, it can be proven that the following equations hold: * $1^l\; =\; 1\; =\; 1^r$ * $x^\; =\; x\; =\; x^$ * $(x\backslash cdot\; y)^l\; =\; y^l\; \backslash cdot\; x^l\; \backslash qquad\; (x\backslash cdot\; y)^r\; =\; y^r\; \backslash cdot\; x^r$ $x^l$ and $x^r$ are called the left and right adjoints of ''x'', respectively. The symbol $\backslash cdot$ and $\backslash leq$ are also written $\backslash otimes$ and $\backslash to$ respectively. In category theory, pregroups are also known as autonomous categories or (non-symmetric) compact closed categories. More typically, $x\; \backslash cdot\; y$ will just be represented by adjacency, i.e. as $xy$. 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「Pregroup grammar」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.