Abstract

The main result of the present paper is that the variable-free fragment of logic K*, the logic with a single K-style modality and its “reflexive and transitive closure,” is EXPTIMEcomplete. It is then shown that this immediately gives EXPTIME-completeness of variable-free fragments of a number of known EXPTIME-complete logics. Our proof contains a general idea of how to construct a polynomial-time reduction of a propositional logic to its n-variable—and even, in the cases of K*, PDL, CTL, ATL, and some others, variable-free—fragments. Complexity of countermodels for such fragments is considered.