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Communication Dans Un Congrès Année : 2003

Deciding Modal Logics through Relational Translations into GF2

Résumé

We provide a simple translation from the satisfiability problem for regular grammar logics with converse into GF 2 , which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This 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 GF 2 , 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 GF 2 .
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Dates et versions

hal-03201443 , version 1 (21-04-2021)

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  • HAL Id : hal-03201443 , version 1

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Stéphane Demri, Hans de Nivelle. Deciding Modal Logics through Relational Translations into GF2. Proceedings of the 3rd Workshop on Methods for Modalities (M4M-3), Carlos Areces; Patrick Blackburn, Sep 2003, Nancy, France. pp.93-108. ⟨hal-03201443⟩
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