Simulating polyadic modal logics by monadic ones

Journal of Symbolic Logic 68 (2):419-462 (2003)

Abstract

We define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic $\Lambda^{sim}$ in the diamond language with each logic Λ in the language with polyadic modal connectives. We prove that this simulation operator transfers several useful properties of modal logics, such as finite/recursive axiomatizability, frame completeness and the finite model property, canonicity and first-order definability

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2009-01-28

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Yde Venema
University of Amsterdam

References found in this work

Varieties of Complex Algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
Reduction of Second‐Order Logic to Modal Logic.S. K. Thomason - 1975 - Mathematical Logic Quarterly 21 (1):107-114.
Categorial Inference and Modal Logic.Natasha Kurtonina - 1998 - Journal of Logic, Language and Information 7 (4):399-411.

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Citations of this work

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.
Algebraic Semantics for Propositional Superposition Logic.Athanassios Tzouvaras - 2020 - Journal of Applied Non-Classical Logics 30 (4):335-366.

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