Modelling of logical systems by means of their fragments

Abstract

This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two variables (often to the one-variable or even variable-free fragments). Also, it is proved that predicate logics are usually reducible to their fragments with one or two unary predicate letters and two or three individual variables. The work describes conditions sufficient for such reductions and provides examples where they fail, establishing non-reducibility in those cases. Furthermore, the work provides new complexity bounds for several logics, results on Kripke-incompleteness of predicate calculi, and analogues of the classical theorems of Church and Trakhtenbrot for the logic of quasiary predicates.