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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