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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 Lambek calculus ： ウィキペディア英語版 Categorial grammar Categorial grammar is a term used for a family of formalisms in natural language syntax motivated by the principle of compositionality and organized according to the view that syntactic constituents should generally combine as functions or according to a function-argument relationship. Most versions of categorial grammar analyze sentence structure in terms of constituencies (as opposed to dependencies) and are therefore phrase structure grammars (as opposed to dependency grammars). ==Basics== A categorial grammar consists of two parts: a lexicon, which assigns a set of types (also called categories) to each basic symbol, and some type inference rules, which determine how the type of a string of symbols follows from the types of the constituent symbols. It has the advantage that the type inference rules can be fixed once and for all, so that the specification of a particular language grammar is entirely determined by the lexicon. A categorial grammar shares some features with the simply typed lambda calculus. Whereas the lambda calculus has only one function type $A\; \backslash rightarrow\; B$, a categorial grammar typically has two function types, one type which is applied on the left, and one on the right. For example, a simple categorial grammar might have two function types $B/A\backslash ,\backslash !$ and $A\backslash backslash\; B$. The first, $B/A\backslash ,\backslash !$, is the type of a phrase that results in a phrase of type $B\backslash ,\backslash !$ when followed (on the right) by a phrase of type $A\backslash ,\backslash !$. The second, $A\backslash backslash\; B\backslash ,\backslash !$, is the type of a phrase that results in a phrase of type $B\backslash ,\backslash !$ when preceded (on the left) by a phrase of type $A\backslash ,\backslash !$. The notation is based upon algebra. A fraction when multiplied by (i.e. concatenated with) its denominator yields its numerator. As concatenation is not commutative, it makes a difference whether the denominator occurs to the left or right. The concatenation must be on the same side as the denominator for it to cancel out. The first and simplest kind of categorial grammar is called a basic categorial grammar, or sometimes an AB-grammar (after Ajdukiewicz and Bar-Hillel). Given a set of primitive types $\backslash text\backslash ,\backslash !$, let $\backslash text(\backslash text)\backslash ,\backslash !$ be the set of types constructed from primitive types. In the basic case, this is the least set such that $\backslash text\backslash subseteq\; \backslash text(\backslash text)$ and if $X,\; Y\backslash in\; \backslash text(\backslash text)$ then $(X/Y),\; (Y\backslash backslash\; X)\; \backslash in\; \backslash text(\backslash text)$. Think of these as purely formal expressions freely generated from the primitive types; any semantics will be added later. Some authors assume a fixed infinite set of primitive types used by all grammars, but by making the primitive types part of the grammar, the whole construction is kept finite. A basic categorial grammar is a tuple $(\backslash Sigma,\; \backslash text,\; S,\; \backslash triangleleft)$ where $\backslash Sigma\backslash ,\backslash !$ is a finite set of symbols, $\backslash text\backslash ,\backslash !$ is a finite set of primitive types, and $S\; \backslash in\; \backslash text(\backslash text)$. The relation $\backslash triangleleft$ is the lexicon, which relates types to symbols $(\backslash triangleleft)\; \backslash subseteq\; \backslash text(\backslash text)\; \backslash times\; \backslash Sigma$. Since the lexicon is finite, it can be specified by listing a set of pairs like $TYPE\backslash triangleleft\backslash text$. Such a grammar for English might have three basic types $(N,NP,\; \backslash text\; S)\backslash ,\backslash !$, assigning count nouns the type $N\backslash ,\backslash !$, complete noun phrases the type $NP\backslash ,\backslash !$, and sentences the type $S\backslash ,\backslash !$. Then an adjective could have the type $N/N\backslash ,\backslash !$, because if it is followed by a noun then the whole phrase is a noun. Similarly, a determiner has the type $NP/N\backslash ,\backslash !$, because it forms a complete noun phrase when followed by a noun. Intransitive verbs have the type $NP\backslash backslash\; S$, and transitive verbs the type $(NP\backslash backslash\; S)/NP$. Then a string of words is a sentence if it has overall type $S\backslash ,\backslash !$. For example, take the string "the bad boy made that mess". Now "the" and "that" are determiners, "boy" and "mess" are nouns, "bad" is an adjective, and "made" is a transitive verb, so the lexicon is , $N\backslash triangleleft\backslash text$, $N\backslash triangleleft\backslash text$, $N/N\backslash triangleleft\backslash text$, $(NP\backslash backslash\; S)/NP\backslash triangleleft\backslash text$}. and the sequence of types in the string is $$ } } } } } } now find functions and appropriate arguments and reduce them according to the two inference rules $X\backslash leftarrow\; X/Y,\backslash ;\; Y$ and $X\backslash leftarrow\; Y,\backslash ;\; Y\backslash backslash\; X$: $.\backslash qquad\; NP/N,\backslash ;\; N/N,\backslash ;\; N,\backslash ;\; (NP\backslash backslash\; S)/NP,\backslash ;\; \backslash underbrace$ $.\backslash qquad\; NP/N,\backslash ;\; N/N,\backslash ;\; N,\backslash ;\; \backslash underbrace$ $.\backslash qquad\; NP/N,\backslash ;\; \backslash underbrace,\; \backslash qquad\; (NP\backslash backslash\; S)$ $.\backslash qquad\; \backslash underbrace,\backslash ;\; \backslash qquad\; (NP\backslash backslash\; S)$ $.\backslash qquad\; \backslash qquad\backslash underbrace$ $.\backslash qquad\; \backslash qquad\backslash qquad\backslash quad\backslash ;\backslash ;\backslash ;\; S$ The fact that the result is $S\backslash ,\backslash !$ means that the string is a sentence, while the sequence of reductions shows that it must be parsed as ((the (bad boy)) (made (that mess))). Categorial grammars of this form (having only function application rules) are equivalent in generative capacity to context-free grammars and are thus often considered inadequate for theories of natural language syntax. Unlike CFGs, categorial grammars are lexicalized, meaning that only a small number of (mostly language-independent) rules are employed, and all other syntactic phenomena derive from the lexical entries of specific words. Another appealing aspect of categorial grammars is that it is often easy to assign them a compositional semantics, by first assigning interpretation types to all the basic categories, and then associating all the derived categories with appropriate function types. The interpretation of any constituent is then simply the value of a function at an argument. With some modifications to handle intensionality and quantification, this approach can be used to cover a wide variety of semantic phenomena. 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「Categorial 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.