In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 221-240 (2002)

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Abstract
We propose a generalization of Sahlqvist formulas to polyadic modal languages by representing such languages in a combinatorial PDL style and thus, in particular, developing what we believe to be the right syntactic approach to Sahlqvist formulas at all. The class of polyadic Sahlqvist formulas PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.
Keywords polyadic modal languages  Sahlqvist formulas  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.
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.
Towards Incorporating Background Theories Into Quantifier Elimination.Andrzej Szalas - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):325-340.

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