Decidable fragments of first-order modal logics

Publisher： Cambridge University Press

E-ISSN： 1943-5886|66|3|1415-1438

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.66, Iss.3, 2001-09, pp. : 1415-1438

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Abstract

The paper considers the set of first-order polymodal formulas the modal operators in which can be applied to subformulas of at most one free variable. Using a mosaic technique, we prove a general satisfiability criterion for formulas in , which reduces the modal satisfiability to the classical one. The criterion is then used to single out a number of new, in a sense optimal, decidable fragments of various modal predicate logics.

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