Journal of Logic and Computation, Volume 11, Issue 5, pp. 737754: Abstract.
Sahlqvist Formulas in Hybrid Polyadic Modal LogicsValentin Goranko^{1}, and Dimiter Vakarelov^{2}
^{1}Department of Mathematics, Rand Afrikaans University, PO Box 524, Auckland Park 2006, Johannesburg, South Africa. Email: vfg@na.rau.ac.za
Building on a new approach to polyadic modal languages and Sahlqvist formulas we define Sahlqvist formulas in hybrid polyadic modal languages containing nominals and universal modality or satisfaction operators. Particularly interesting is the case of reversive polyadic languages, closed under all `inverses' of polyadic modalities because the minimal valuations arising in the computation of the firstorder equivalents of polyadic Sahlqvist formulae are definable in such languages and that makes the proof of firstorder definability and canonicity of these formulas a simple syntactic exercise. Furthermore, the firstorder definability of Sahlqvist formulas immediately transfers to arbitrary polyadic languages, while the direct transfer of canonicity requires a more involved prooftheoretic analysis.
Keywords: Hybrid polyadic modal logics, Sahlqvist formulas, nominals, universal modality, satisfaction operator, first, order definability, canonicity, completeness
