Abstract
A problem of recognizing important properties of propositional calculi is considered, and complexity bounds for some decidable properties are found. 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 Maksimova and Voronkov (Bull. Symbol. Logic 6 (2000) 118) the complexity of tabularity, pretabularity, and interpolation problems over the intuitionistic logic (Int) and over modal logic S4 was studied. In the present paper, positive and positively axiomatizable calculi are investigated. We prove NP-completeness of tabularity, DP-hardness of pretabularity and PSPACE-completeness of interpolation and projective Beth's property over the positive fragment Int + of the intuitionistic logic. Some complexity bounds for properties of propositional calculi over the intuitionistic or the minimal logic are found.
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