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2007 Semantical Characterizations for Irreflexive and Generalized Modal Languages
SANO Katsuhiko, SATO Kentaro
Notre Dame J. Formal Logic 48(2): 205-228 (2007). DOI: 10.1305/ndjfl/1179323264

Abstract

This paper deals with two main topics: One is a semantical investigation for a bimodal language with a modal operator \blacksquare associated with the intersection of the accessibility relation R and the inequality ≠. The other is a generalization of some of the former results to general extended languages with modal operators. First, for our language L\sb{\square\blacksquare}, we prove that Segerberg's theorem (equivalence between finite frame property and finite model property) fails and establish both van Benthem-style and Goldblatt-Thomason-style characterizations. We extract the notion of \blacksquare-realizer (a generalization of bulldozing) as an essence from the proofs of our results. Second, we generalize the notion of \blacksquare-realizer and prove quite general versions of these semantical characterization results. The known and previously unknown characterization results for almost all of the languages extended with modal operators already proposed will be immediate corollaries.

Citation

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SANO Katsuhiko. SATO Kentaro. "Semantical Characterizations for Irreflexive and Generalized Modal Languages." Notre Dame J. Formal Logic 48 (2) 205 - 228, 2007. https://doi.org/10.1305/ndjfl/1179323264

Information

Published: 2007
First available in Project Euclid: 16 May 2007

zbMATH: 1131.03009
MathSciNet: MR2306393
Digital Object Identifier: 10.1305/ndjfl/1179323264

Subjects:
Primary: 03B45
Secondary: 03B44, 03C40

Rights: Copyright © 2007 University of Notre Dame

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Vol.48 • No. 2 • 2007
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