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 "Complexity of some problems in modal and superintuitionistic logics," 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.
Citation
Larisa Maksimova. "Complexity of interpolation and related problems in positive calculi." J. Symbolic Logic 67 (1) 397 - 408, March 2002. https://doi.org/10.2178/jsl/1190150051
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