Deciding Modal Logics through Relational Translations into GF2

de Nivelle, Hans; Demri, Stéphane; Areces, Carlos; Blackburn, Patrick

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Deciding Modal Logics through Relational Translations into GF2

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de Nivelle, Hans
Programming Logics, MPI for Informatics, Max Planck Society;

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de Nivelle, H., & Demri, S. (2003). Deciding Modal Logics through Relational Translations into GF2. In Proceedings of the 3rd Methods for Modalities Workshop (pp. 15-30). Nancy, France: Loria.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-2CAF-A

Abstract

We provide a simple translation from the satisfiability problem for regular grammar logics with converse into {GF2}, the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. Using the same method, one can show that other modal logics can be naturally translated into {GF2}, including nominal tense logics and intuitionistic propositional logic. In our view, the results in this paper provide strong evidence that the natural first-order fragment corresponding to modal logics, is {GF2}.