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• Herbrandization

Proof of Herbrand's theorem

The Herbrandization of a logical formula (named after Jacques Herbrand) is a construction that is dual to the Skolemization of a formula. Thoralf Skolem

Herbrandization

Herbrandization

• Herbrand's theorem

Fundamental result of mathematical logic

can be removed by Herbrandization. Conversion to prenex form can be avoided, if structural Herbrandization is performed. Herbrandization can be avoided by

Herbrand's theorem

Herbrand's_theorem

• First-order logic

Type of logical system

Ehrenfeucht-Fraisse game Extension by definitions Extension (predicate logic) Herbrandization List of logic symbols Lojban Löwenheim number Nonfirstorderizability

First-order logic

First-order_logic

• Skolem normal form

Formalism of first-order logic

form is named after the late Norwegian mathematician Thoralf Skolem. Herbrandization, the dual of Skolemization Predicate functor logic "Normal Forms and

Skolem normal form

Skolem_normal_form

• DPLL algorithm

Type of search algorithm

correspond to tree resolution refutation proofs. Proof complexity Herbrandization General Davis, Martin; Putnam, Hilary (1960). "A Computing Procedure

DPLL algorithm



DPLL_algorithm

• Prenex normal form

Formalism of first-order logic

prenex in Wiktionary, the free dictionary. Arithmetical hierarchy Herbrandization Skolemization The term 'prenex' comes from the Latin praenexus "tied

Prenex normal form

Prenex_normal_form

• Davis–Putnam algorithm

Check the validity of a logic formula

basis for today's (as of 2015) most efficient complete SAT solvers. Herbrandization DPLL algorithm Davis, Martin; Putnam, Hilary (1960). "A Computing Procedure

Davis–Putnam algorithm

Davis–Putnam_algorithm

• Herbrand structure

Structure over a vocabulary defined solely by syntactical properties

c),R(fc,c),R(c,fc),R(fc,fc),R(ffc,c),\dots \}} Herbrand's theorem Herbrandization Herbrand interpretation "Herbrand Semantics". Archived from the original

Herbrand structure

Herbrand_structure

• Jacques Herbrand

French mathematician (1908–1931)

Herbrand – by the French Academy of Sciences, for mathematics and physics Herbrandization – a validity-preserving normal form of a formula, dual to Skolemization

Jacques Herbrand



Jacques_Herbrand

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