Journal of Applied Logic 8 (4):319-333 (2010)

Authors
Valentin Goranko
Stockholm University
Abstract
The previously introduced algorithm \sqema\ computes first-order frame equivalents for modal formulae and also proves their canonicity. Here we extend \sqema\ with an additional rule based on a recursive version of Ackermann's lemma, which enables the algorithm to compute local frame equivalents of modal formulae in the extension of first-order logic with monadic least fixed-points \mffo. This computation operates by transforming input formulae into locally frame equivalent ones in the pure fragment of the hybrid mu-calculus. In particular, we prove that the recursive extension of \sqema\ succeeds on the class of `recursive formulae'. We also show that a certain version of this algorithm guarantees the canonicity of the formulae on which it succeeds.
Keywords Modal logic  correspondence theory   canonicity   first-order logic with fixed-points  algorithm SQEMA
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DOI 10.1016/j.jal.2010.08.002
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Modal Logic and Classical Logic.Johan van Benthem - 1983 - Distributed in the U.S.A. By Humanities Press.
Modal Logic and Classical Logic.R. A. Bull - 1987 - Journal of Symbolic Logic 52 (2):557-558.

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