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Classical Gentzen-type Methods in Propositional Many-valued Logics

  • Arnon Avron
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 114)

Abstract

A classical Gentzen-type system is one which employs two-sided sequents, together with structural and logical rules of a certain characteristic form. A decent Gentzen-type system should allow for direct proofs, which means that it should admit some useful forms of cut elimination and the subformula property. In this survey we explain the main difficulty in developing classical Gentzen-type systems with these properties for many-valued logics. We then illustrate with numerous examples the various possible ways of overcoming this difficulty, and the strong connection between semantic completeness and cut-elimination in each case. Our examples include practically all 3-valued and 4-valued logics, as well as Gödel finite-valued logics and some well-known infinite-valued logics.

Keywords

Atomic Formula Strong Completeness Propositional Constant Strong Soundness Subformula Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Arnon Avron
    • 1
  1. 1.School of Computer ScienceTel-Aviv UniversityRamat AvivIsrael

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