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In logic, especially mathematical logic, a signature lists and describes the non-logical symbols of a formal language. In universal algebra, a signature lists the operations that characterize an algebraic structure. In model theory, signatures are used for both purposes. Signatures play the same role in mathematics as type signatures in computer programming. They are rarely made explicit in more philosophical treatments of logic. == Definition == Formally, a (single-sorted) signature can be defined as a triple σ = (''S''func, ''S''rel, ar), where ''S''func and ''S''rel are disjoint sets not containing any other basic logical symbols, called respectively * ''function symbols'' (examples: +, ×, 0, 1) and * ''relation symbols'' or ''predicates'' (examples: ≤, ∈), and a function ar: ''S''func ''S''rel → which assigns a non-negative integer called ''arity'' to every function or relation symbol. A function or relation symbol is called ''n''-ary if its arity is ''n''. A nullary (''0''-ary) function symbol is called a ''constant symbol''. A signature with no function symbols is called a relational signature, and a signature with no relation symbols is called an algebraic signature. A finite signature is a signature such that ''S''func and ''S''rel are finite. More generally, the cardinality of a signature σ = (''S''func, ''S''rel, ar) is defined as |σ| = |''S''func| + |''S''rel|. The language of a signature is the set of all well formed sentences built from the symbols in that signature together with the symbols in the logical system. 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「Signature (logic)」の詳細全文を読む スポンサード リンク
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