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Sahlqvist Formulas Unleashed in Polyadic Modal Languages

In Frank Wolter, Heinrich Wansing, Maarten de Rijke & Michael Zakharyaschev (eds.), Advances in Modal Logic, Volume 3. World Scientific. pp. 221-240 (2002)

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  1. Algorithmic Correspondence and Completeness in Modal Logic. V. Recursive Extensions of SQEMA.Willem Conradie, Valentin Goranko & Dimitar Vakarelov - 2010 - Journal of Applied Logic 8 (4):319-333.
    The previously introduced algorithm \sqema\ computes first-order frame equivalents for modal formulae and also proves their canonicity. Here we extend \sqema\ with an additional rule based on a recursive version of Ackermann's lemma, which enables the algorithm to compute local frame equivalents of modal formulae in the extension of first-order logic with monadic least fixed-points \mffo. This computation operates by transforming input formulae into locally frame equivalent ones in the pure fragment of the hybrid mu-calculus. In particular, we prove that (...)
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  • Sahlqvist Theorems for Precontact Logics.Philippe Balbiani & Stanislav Kikot - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic. CSLI Publications. pp. 55-70.
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  • Semantic Characterization of Krancht Formulas.Stanislav Kikot - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic, Volume 8. CSLI Publications. pp. 218-234.
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  • An Extension of Kracht's Theorem to Generalized Sahlqvist Formulas.Stanislav Kikot - 2009 - Journal of Applied Non-Classical Logics 19 (2):227-251.
    Sahlqvist formulas are a syntactically specified class of modal formulas proposed by Hendrik Sahlqvist in 1975. They are important because of their first-order definability and canonicity, and hence axiomatize complete modal logics. The first-order properties definable by Sahlqvist formulas were syntactically characterized by Marcus Kracht in 1993. The present paper extends Kracht's theorem to the class of ‘generalized Sahlqvist formulas' introduced by Goranko and Vakarelov and describes an appropriate generalization of Kracht formulas.
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