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The Bernays–Schönfinkel class (also known as Bernays–Schönfinkel–Ramsey class) of formulas, named after Paul Bernays, Moses Schönfinkel and Frank P. Ramsey, is a fragment of first-order logic formulas where satisfiability is decidable. It is the set of sentences that, when written in prenex normal form, have an quantifier prefix and do not contain any function symbols. This class of logic formulas is also sometimes referred as effectively propositional (EPR) since it can be effectively translated into propositional logic formulas by a process of grounding or instantiation.

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  • Bernays–Schönfinkel class (en)
  • Classe de Bernays-Schönfinkel (fr)
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  • The Bernays–Schönfinkel class (also known as Bernays–Schönfinkel–Ramsey class) of formulas, named after Paul Bernays, Moses Schönfinkel and Frank P. Ramsey, is a fragment of first-order logic formulas where satisfiability is decidable. It is the set of sentences that, when written in prenex normal form, have an quantifier prefix and do not contain any function symbols. This class of logic formulas is also sometimes referred as effectively propositional (EPR) since it can be effectively translated into propositional logic formulas by a process of grounding or instantiation. (en)
  • En logique mathématique, la classe de Bernays-Schönfinkel (parfois appelée la classe de Bernays-Schönfinkel-Ramsey) est le fragment syntaxique de la logique du premier ordre des formules dont la forme prénexe est de la forme et qui ne contiennent pas de symboles de fonctions. Elle est nommée d'après ses créateurs, Paul Bernays et Moses Schönfinkel (avec l'apport aussi de Frank Ramsey). Le problème de la satisfiabilité est décidable et NEXPTIME-complet. (fr)
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  • The Bernays–Schönfinkel class (also known as Bernays–Schönfinkel–Ramsey class) of formulas, named after Paul Bernays, Moses Schönfinkel and Frank P. Ramsey, is a fragment of first-order logic formulas where satisfiability is decidable. It is the set of sentences that, when written in prenex normal form, have an quantifier prefix and do not contain any function symbols. This class of logic formulas is also sometimes referred as effectively propositional (EPR) since it can be effectively translated into propositional logic formulas by a process of grounding or instantiation. The satisfiability problem for this class is NEXPTIME-complete. (en)
  • En logique mathématique, la classe de Bernays-Schönfinkel (parfois appelée la classe de Bernays-Schönfinkel-Ramsey) est le fragment syntaxique de la logique du premier ordre des formules dont la forme prénexe est de la forme et qui ne contiennent pas de symboles de fonctions. Elle est nommée d'après ses créateurs, Paul Bernays et Moses Schönfinkel (avec l'apport aussi de Frank Ramsey). Le problème de la satisfiabilité est décidable et NEXPTIME-complet. Cette classe de formules s'appelle parfois effectively propositional (EPR) car elle peut être effectivement traduite en logique propositionnelle en instanciant les variables universelles par des termes clos. (fr)
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