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Uniform Cut-Free Bisequent Calculi for Three-Valued Logics.

We present a uniform characterisation of three-valued logics by means of a bisequent calculus (BSC). It is a generalised form of a sequent calculus (SC) where rules operate on the ordered pairs of ordinary sequents. BSC may be treated as the weakest kind of system in the rich family of generalised S...

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Published in:Logic & Logical Philosophy Vol. 33; no. 3; pp. 463 - 507
Main Authors: Indrzejczak, Andrzej, Petrukhin, Yaroslav
Format: Article
Published: Logic & Logical Philosophy Sep2024
Subjects:
Many-valued logic
Calculi
Calculus
Logic
Generalization
Online Access:View this record in EBSCOhost
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      dt: Sep2024
      vid: 33
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      pub: Logic & Logical Philosophy
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        180513353
        10.12775/LLP.2024.019
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        atl: Uniform Cut-Free Bisequent Calculi for Three-Valued Logics.
      aug:
        au:
          Indrzejczak, Andrzej
          Petrukhin, Yaroslav
        affil:
          Department of Logic, Institute of Philosophy, University of Łódź, Poland
          Center for Philosophy of Nature, University of Łódź, Poland
      su:
        Many-valued logic
        Calculi
        Calculus
        Logic
        Generalization
      sug:
        subj:
          Many-valued logic
          Calculi
          Calculus
          Logic
          Generalization
      keyword:
        bisequent calculus
        cut elimination
        interpolation theorem
        many-valued logic
        threevalued logic
      ab: We present a uniform characterisation of three-valued logics by means of a bisequent calculus (BSC). It is a generalised form of a sequent calculus (SC) where rules operate on the ordered pairs of ordinary sequents. BSC may be treated as the weakest kind of system in the rich family of generalised SC operating on items being some collections of ordinary sequents, like hypersequent and nested sequent calculi. It seems that for many non-classical logics, including some many-valued, paraconsistent and modal logics, the reasonably modest generalisation of standard SC offered by BSC is sufficient. In this paper, we examine a variety of three-valued logics and show how they can be formalised in the framework of BSC. We present a constructive syntactic proof that these systems are cut-free, satisfy the subformula property, and allow one to prove the interpolation theorem in many cases.
      pubtype: Academic Journal
      doctype: Article
      src: R
    language: English
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