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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}.
