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March 2002 Complexity of interpolation and related problems in positive calculi
Larisa Maksimova
J. Symbolic Logic 67(1): 397-408 (March 2002). DOI: 10.2178/jsl/1190150051

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.

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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

Information

Published: March 2002
First available in Project Euclid: 18 September 2007

zbMATH: 1037.03005
MathSciNet: MR1889558
Digital Object Identifier: 10.2178/jsl/1190150051

Subjects:
Primary: 03B20
Secondary: 03C40 , 03D15 , 68Q15

Rights: Copyright © 2002 Association for Symbolic Logic

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Vol.67 • No. 1 • March 2002
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