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Inference Rules in Nelson’s Logics, Admissibility and Weak Admissibility

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Abstract

Our paper aims to investigate inference rules for Nelson’s logics and to discuss possible ways to determine admissibility of inference rules in such logics. We will use the technique offered originally for intuitionistic logic and paraconsistent minimal Johannson’s logic. However, the adaptation is not an easy and evident task since Nelson’s logics do not enjoy replacement of equivalences rule. Therefore we consider and compare standard admissibility and weak admissibility. Our paper founds algorithms for recognizing weak admissibility and admissibility itself – for restricted cases, to show the problems arising in the course of study.

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Authors and Affiliations

  1. Institute of Mathematics, 4 Acad. Koptyug avenue, 630090, Novosibirsk, Russian Federation

    Sergei Odintsov

  2. School of Computing, Mathematics and DT, Manchester Metropolitan University, John Dalton Building, Chester Street, Manchester, M1 5GD, UK

    Vladimir Rybakov

Authors
  1. Sergei Odintsov
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  2. Vladimir Rybakov
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Correspondence to Sergei Odintsov.

Additional information

This work was supported by Russian Foundation for Basic Research, Project No. 12-01-00168-a.

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Odintsov, S., Rybakov, V. Inference Rules in Nelson’s Logics, Admissibility and Weak Admissibility. Log. Univers. 9, 93–120 (2015). https://doi.org/10.1007/s11787-014-0110-8

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  • DOI: https://doi.org/10.1007/s11787-014-0110-8

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