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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 Theory (mathematical logic) ： ウィキペディア英語版 Theory (mathematical logic) In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. Usually a deductive system is understood from context. An element $\backslash phi\backslash in\; T$ of a theory $T$ is then called an axiom of the theory, and any sentence that follows from the axioms ($T\backslash vdash\backslash phi$) is called a theorem of the theory. Every axiom is also a theorem. A first-order theory is a set of first-order sentences. == Theories expressed in formal language generally == When defining theories for foundational purposes, additional care must be taken and normal set-theoretic language may not be appropriate. The construction of a theory begins by specifying a definite non-empty ''conceptual class'' $\backslash mathcal$, the elements of which are called ''statements''. These initial statements are often called the ''primitive elements'' or ''elementary'' statements of the theory, to distinguish them from other statements which may be derived from them. A theory $\backslash mathcal$ is a conceptual class consisting of certain of these elementary statements. The elementary statements which belong to $\backslash mathcal$ are called the ''elementary theorems'' of $\backslash mathcal$ and said to be ''true''. In this way, a theory is a way of designating a subset of $\backslash mathcal$ which consists entirely of true statements. This general way of designating a theory stipulates that the truth of any of its elementary statements is not known without reference to $\backslash mathcal$. Thus the same elementary statement may be true with respect to one theory, and not true with respect to another. This is as in ordinary language, where statements such as "He is a terrible person." cannot be judged to be true or false without reference to some interpretation of who "He" is and for that matter what a "terrible person" is under this theory.〔Curry, Haskell, ''Foundations of Mathematical 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「Theory (mathematical logic)」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.