Sahlqvist Formulas in Hybrid Polyadic Modal Logics

Abstract

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 first‐order equivalents of polyadic Sahlqvist formulae are definable in such languages and that makes the proof of first‐order definability and canonicity of these formulas a simple syntactic exercise. Furthermore, the first‐order definability of Sahlqvist formulas immediately transfers to arbitrary polyadic languages, while the direct transfer of canonicity requires a more involved proof‐theoretic analysis.