Abstract

We consider the problem of recognizing important properties of logical calculi and find complexity bounds for some decidable properties. For a given logical system L, a property P of logical calculi is called decidable over L if there is an algorithm which for any finite set Ax of new axiom schemes decides whether the calculus L + Ax has the property P or not. In [11] the complexity of tabularity, pre-tabularity, and interpolation problems over the intuitionistic logic Int and over modal logic S4 was studied, also we found the complexity of amalgamation problems in varieties of Heyting algebras and closure algebras. In the present paper we deal with positive calculi. We prove NP-completeness of tabularity, DP-hardness of pretabularity and PSPACE-completeness of interpolation problem over Int + . In addition to above-mentioned properties, we consider Beth's definability properties. Also we improve some complexity bounds for properties of superintuitionistic calculi