Annals of Pure and Applied Logic 141 (1):180-217 (2006)

We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive formulae are elementary canonical and thus extend Sahlqvist’s theorem over them. In particular, we give a simple example of an inductive formula which is not frame-equivalent to any Sahlqvist formula. Then, after a deeper analysis of the inductive formulae as set-theoretic operators in descriptive and Kripke frames, we establish a somewhat stronger model-theoretic characterization of these formulae in terms of a suitable equivalence to syntactically simpler formulae in the extension of the language with reversive modalities. Lastly, we study and characterize the elementary canonical formulae in reversive languages with nominals, where the relevant notion of persistence is with respect to discrete frames
Keywords polyadic modal languages  Sahlqvist formulae  inductive formulae  elementary canonical formulae  Correspondence theory
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DOI 10.1016/j.apal.2005.10.005
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References found in this work BETA

Modal Logic with Names.George Gargov & Valentin Goranko - 1993 - Journal of Philosophical Logic 22 (6):607 - 636.
Varieties of Complex Algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
A Sahlqvist Theorem for Distributive Modal Logic.Mai Gehrke, Hideo Nagahashi & Yde Venema - 2004 - Annals of Pure and Applied Logic 131 (1-3):65-102.
Derivation Rules as Anti-Axioms in Modal Logic.Yde Venema - 1993 - Journal of Symbolic Logic 58 (3):1003-1034.
Topology and Duality in Modal Logic.Giovanni Sambin & Virginia Vaccaro - 1988 - Annals of Pure and Applied Logic 37 (3):249-296.

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Citations of this work BETA

Minimal Predicates, Fixed-Points, and Definability.Johan van Benthem - 2005 - Journal of Symbolic Logic 70 (3):696-712.
The Bounded Proof Property Via Step Algebras and Step Frames.Nick Bezhanishvili & Silvio Ghilardi - 2014 - Annals of Pure and Applied Logic 165 (12):1832-1863.

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