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Journal of Logic and Computation, Volume 11, Issue 5, pp. 737-754: Abstract.

Sahlqvist Formulas in Hybrid Polyadic Modal Logics

Valentin Goranko1, and Dimiter Vakarelov2

1Department of Mathematics, Rand Afrikaans University, PO Box 524, Auckland Park 2006, Johannesburg, South Africa. E-mail: vfg@na.rau.ac.za
2Faculty of Mathematics and Computer Science, Sofia University, blvd. James Bouchier 5, 1126 Sofia, Bulgaria. E-mail: dvak@fmi.uni-sofia.bg

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.

Keywords: Hybrid polyadic modal logics, Sahlqvist formulas, nominals, universal modality, satisfaction operator, first-, order definability, canonicity, completeness

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