Products of modal logics. Part 2: relativised quantifiers in classical logic

Logic Journal of the IGPL 8 (2):165-210 (2000)
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Abstract

In the first part of this paper we introduced products of modal logics and proved basic results on their axiomatisability and the f.m.p. In this continuation paper we prove a stronger result - the product f.m.p. holds for products of modal logics in which some of the modalities are reflexive or serial. This theorem is applied in classical first-order logic, we identify a new Square Fragment of the classical logic, where the basic predicates are binary and all quantifiers are relativised, and for which we show the f.m.p. in the classical sense. Also we prove that SF not included in Guarded Fragment and that it can be embedded into the equational theory of relational algebras

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Author Profiles

Valentin Shehtman
Moscow State University
Dov Gabbay
Hebrew University of Jerusalem

Citations of this work

On Modal Logics of Hamming Spaces.Andrey Kudinov, Ilya Shapirovsky & Valentin Shehtman - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 395-410.
Axiomatization and completeness of lexicographic products of modal logics.Philippe Balbiani - 2011 - Journal of Applied Non-Classical Logics 21 (2):141-176.

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References found in this work

The axiomatization of randomness.Michiel van Lambalgen - 1990 - Journal of Symbolic Logic 55 (3):1143-1167.

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