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In mathematical logic, a well-formed formula, shortly wff, often simply formula, is a word (i.e. a finite sequence of symbols from a given alphabet) that is part of a formal language.〔Formulas are a standard topic in introductory logic, and are covered by all introductory textbooks, including Enderton (2001), Gamut (1990), and Kleene (1967)〕 A formal language can be considered to be identical to the set containing all and only its formulas. A formula is a syntactic formal object that can be given a semantic meaning by means of semantics. ==Introduction== A key use of formulae is in propositional logic and predicate logics such as first-order logic. In those contexts, a formula is a string of symbols φ for which it makes sense to ask "is φ true?", once any free variables in φ have been instantiated. In formal logic, proofs can be represented by sequences of formulas with certain properties, and the final formula in the sequence is what is proven. Although the term "formula" may be used for written marks (for instance, on a piece of paper or chalkboard), it is more precisely understood as the sequence being expressed, with the marks being a token instance of formula. It is not necessary for the existence of a formula that there be any actual tokens of it. A formal language may thus have an infinite number of formulas regardless whether each formula has a token instance. Moreover, a single formula may have more than one token instance, if it is written more than once. Formulas are quite often interpreted as propositions (as, for instance, in propositional logic). However formulas are syntactic entities, and as such must be specified in a formal language without regard to any interpretation of them. An interpreted formula may be the name of something, an adjective, an adverb, a preposition, a phrase, a clause, an imperative sentence, a string of sentences, a string of names, etc.. A formula may even turn out to be nonsense, if the symbols of the language are specified so that it does. Furthermore, a formula need not be given ''any'' interpretation. 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「Well-formed formula」の詳細全文を読む スポンサード リンク
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