prenex formula
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Prenex normal form — A formula of the predicate calculus is in prenex[1] normal form if it is written as a string of quantifiers followed by a quantifier free part (referred to as the matrix). Every formula in classical logic is equivalent to a formula in prenex… … Wikipedia
prenex — adjective Of a formula, having all of its quantifiers at the beginning. We say that is universal iff it can be written in prenex form mdash; i.e. with all quantifiers at the beginning mdash; using only universal quantifiers … Wiktionary
prenex normal form — A well formed formula of the predicate calculus is in prenex normal form if all the quantifiers stand at the front, and any other logical constant stands within the scope of all the quantifiers … Philosophy dictionary
prenex normal form — ˈprēˌneks noun Etymology: Late Latin praenexus tied up or bound in front, from Latin prae pre + nexus, past participle of nectere to tie, bind more at annex : a normal form of an expression in the functional calculus in which all the quantifiers… … Useful english dictionary
True quantified Boolean formula — The language TQBF is a formal language in computer science that contains True Quantified Boolean Formulas. A fully quantified boolean formula is a formula in first order logic where every variable is quantified (or bound), using either… … Wikipedia
Original proof of Gödel's completeness theorem — The proof of Gödel s completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a rewritten version of the dissertation, published as an article in 1930) is not easy to read today; it uses concepts and formalism that are… … Wikipedia
Skolem normal form — A formula of first order logic is in Skolem normal form (named after Thoralf Skolem) if it is in conjunctive prenex normal form with only universal first order quantifiers. Every first order formula can be converted into Skolem normal form while… … Wikipedia
Herbrand's theorem — is a fundamental result of mathematical logic obtained by Jacques Herbrand (1930). [J. Herbrand: Recherches sur la theorie de la demonstration. Travaux de la Societe des Sciences et des Lettres de Varsovie, Class III, Sciences Mathematiques et… … Wikipedia
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… … Wikipedia
Herbrandization — The Herbrandization of a logical formula (named after Jacques Herbrand) is a construction that is dual to the Skolemization of a formula. Thoralf Skolem had considered the Skolemizations of formulas in prenex form as part of his proof of the… … Wikipedia
Rules of passage (logic) — In mathematical logic, the rules of passage govern how quantifiers distribute over the basic logical connectives of first order logic. The rules of passage govern the passage (translation) from any formula of first order logic to the equivalent… … Wikipedia
