Abstract

Let a logical propositional calculus L0 be given. We consider arbitrary extensions of L0 by adding finitely many new axiom schemes and rules of inference. We say that a property of P of logical calculi is strongly decidable over L0 if there is an algorithm which for any finite system Rul of axiom schemes and rules of inference decides whether the system L0 + Rul has the property P or not. We consider only so-called structural rules of inference which are invariant under substitution. We remind that P is called decidable over L0 if there is such an algorithm for extensions of L0 with finitely many axiom schemes . In our paper we give a method of proving strong decidability results.We take as L0 some standard calculus for intuitionistic propositional logic Int or modal logic S4 and find a number of properties strongly decidable over L0, in particular, equivalence to some known logic, pretabularity, interpolation property over Int, local tabularity over S4, which are known to be decidable. Some complexity bounds are also given