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 Algebra Logika: Year: Volume: Issue: Page: Find

 Algebra Logika, 2009, Volume 48, Number 6, Pages 754–792 (Mi al423)

Decidability of the interpolation problem and of related properties in tabular logics

L. L. Maksimovaab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: Propositional modal and positive logics are considered as well as extensions of Johansson's minimal logic. It is proved that basic versions of the interpolation property and of the Beth definability property, and also the Hallden property, are decidable on the class of tabular logics, i.e., logics given by finitely many finite algebras. Algorithms are described for constructing counterexamples to each of the properties mentioned in handling cases where the logic under consideration does not possess the required property.

Keywords: decidability, tabular logics, interpolation property, Beth definability property, Hallden property.

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English version:
Algebra and Logic, 2009, 48:6, 426–448

Bibliographic databases:

UDC: 510.64

Citation: L. L. Maksimova, “Decidability of the interpolation problem and of related properties in tabular logics”, Algebra Logika, 48:6 (2009), 754–792; Algebra and Logic, 48:6 (2009), 426–448

Citation in format AMSBIB
\Bibitem{Mak09} \by L.~L.~Maksimova \paper Decidability of the interpolation problem and of related properties in tabular logics \jour Algebra Logika \yr 2009 \vol 48 \issue 6 \pages 754--792 \mathnet{http://mi.mathnet.ru/al423} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2640964} \zmath{https://zbmath.org/?q=an:1241.03032} \transl \jour Algebra and Logic \yr 2009 \vol 48 \issue 6 \pages 426--448 \crossref{https://doi.org/10.1007/s10469-009-9070-0} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000273168500004} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77949275777} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. V. Karpenko, “Interpolation properties in the extensions of the logic of inequality”, Siberian Math. J., 51:3 (2010), 439–451
2. L. L. Maksimova, “Decidability of the weak interpolation property over the minimal logic”, Algebra and Logic, 50:2 (2011), 106–132
3. A. V. Karpenko, “Interpolation in weakly transitive modal logics”, Algebra and Logic, 51:2 (2012), 131–143
4. Odintsov S. Rybakov V., “Unification and Admissible Rules for Paraconsistent Minimal Johanssons' Logic J and Positive Intuitionistic Logic Ipc+”, Ann. Pure Appl. Log., 164:7-8 (2013), 771–784
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