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In modal logic, Sahlqvist formulas are a certain kind of modal formula with remarkable properties. The Sahlqvist correspondence theorem states that every formula is canonical, and corresponds to a first-order definable class of Kripke frames.

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  • Formule de Sahlqvist (fr)
  • Sahlqvist formula (en)
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  • En logique modale, les formules de Sahlqvist (du nom du mathématicien norvégien ) constituent une classe de formules modales assortie de propriétés remarquables. Le théorème de correspondance de Sahlqvist affirme que toute formule de Sahlqvist est canonique (au sens de la sémantique de Kripke) et correspond à une classe de cadres de Kripke caractérisable par une formule en logique du premier ordre décrivant une propriété de la relation d'accessibilité. (fr)
  • In modal logic, Sahlqvist formulas are a certain kind of modal formula with remarkable properties. The Sahlqvist correspondence theorem states that every formula is canonical, and corresponds to a first-order definable class of Kripke frames. (en)
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  • En logique modale, les formules de Sahlqvist (du nom du mathématicien norvégien ) constituent une classe de formules modales assortie de propriétés remarquables. Le théorème de correspondance de Sahlqvist affirme que toute formule de Sahlqvist est canonique (au sens de la sémantique de Kripke) et correspond à une classe de cadres de Kripke caractérisable par une formule en logique du premier ordre décrivant une propriété de la relation d'accessibilité. (fr)
  • In modal logic, Sahlqvist formulas are a certain kind of modal formula with remarkable properties. The Sahlqvist correspondence theorem states that every formula is canonical, and corresponds to a first-order definable class of Kripke frames. Sahlqvist's definition characterizes a decidable set of modal formulas with first-order correspondents. Since it is undecidable, by Chagrova's theorem, whether an arbitrary modal formula has a first-order correspondent, there are formulas with first-order frame conditions that are not Sahlqvist [Chagrova 1991] (see the examples below). Hence Sahlqvist formulas define only a (decidable) subset of modal formulas with first-order correspondents. (en)
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