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

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Algebra and Logic Aims and scope

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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    L. L. Maksimova

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    L. L. Maksimova

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  1. L. L. Maksimova
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Correspondence to L. L. Maksimova.

Additional information

Supported by RFBR (project No. 09-01-00090a), by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-335.2008.1), and by the Russian Ministry of Education through the Analytical Departmental Target Program (ADTP) “Development of Scientific Potential of the Higher School of Learning” (project No. 2.1.1.419).

Translated from Algebra i Logika, Vol. 48, No. 6, pp. 754-792, November-December, 2009.

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Maksimova, L.L. Decidability of the interpolation problem and of related properties in tabular logics. Algebra Logic 48, 426–448 (2009). https://doi.org/10.1007/s10469-009-9070-0

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  • DOI: https://doi.org/10.1007/s10469-009-9070-0

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