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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Abstract
We propose a generalization of Sahlqvist formulae to polyadic modal languages by representing modal polyadic languages in a combinatorial style and thus, in particular, developing what we believe to be the right approach to Sahlqvist formulae at all. The class of polyadic Sahlqvist formulae PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.
Keywords polyadic modal logic  polyadic Sahlqvist formulae  first-order definability  canonicity
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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 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.
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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