“first-order logic”的概念、定义、翻译、参考文献-科学参考

first-order logic

Mathematics

In propositional logic, sentences do not involve quantifiers; for example, De Morgan’s Laws are laws of propositional logic. Also known as predicate logic, first-order logic is an extension of propositional logic which permits quantifiers over elements; for example, (∀x∈ℝ)(∃y∈ℝ)(x + y = 0) states that every real number has an additive inverse. But the completeness axiom for ℝ, that every non-empty, bounded-above subset of ℝ has a supremum, necessarily involves quantification over subsets of ℝ, and so is a second-order sentence.

Computer

Logic

A form of logic for a language including the quantifiers $\forall$ or $\exists$ , whose bound variables stand in name places, as in $\exists x \neg P x$ or $\exists x \forall y Rxy$ .

Philosophy

单词	first-order logic
释义	first-order logic Mathematics In propositional logic, sentences do not involve quantifiers; for example, De Morgan’s Laws are laws of propositional logic. Also known as predicate logic, first-order logic is an extension of propositional logic which permits quantifiers over elements; for example, (∀x∈ℝ)(∃y∈ℝ)(x + y = 0) states that every real number has an additive inverse. But the completeness axiom for ℝ, that every non-empty, bounded-above subset of ℝ has a supremum, necessarily involves quantification over subsets of ℝ, and so is a second-order sentence. Computer Another name for predicate calculus. Logic A form of logic for a language including the quantifiers $\forall$ or $\exists$ , whose bound variables stand in name places, as in $\exists x \neg P x$ or $\exists x \forall y Rxy$ . Philosophy The study of inference in first-order languages.
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