| 释义 |
first-order logic 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.
|