出典:Wiktionary
first-order logic (countable かつ uncountable, 複数形 first-order logics)
出典:Wikipedia
出典:『Wikipedia』 (2011/06/18 20:40 UTC 版)
First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less precise term). First-order logic is distinguished from propositional logic by its use of quantifiers; each interpretation of first-order logic includes a domain of discourse over which the quantifiers range. The adjective "first-order" is used to distinguish first-order theories from higher-order theories in which there are predicates having other predicates or functions as arguments or in which predicate quantifiers or function quantifiers are permitted or both. In interpretations of first-order theories predicates are associated with sets. In interpretations of higher order theories they may be also associated with sets of sets.