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Pavelka-style completeness in expansions of Łukasiewicz logic

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Abstract

An algebraic setting for the validity of Pavelka style completeness for some natural expansions of Łukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard MV-algebra on the real segment [0, 1] is an injective MV-algebra. In particular the logics associated with MV-algebras with product and with divisible MV-algebras are considered.

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Authors and Affiliations

  1. Dipartimento di Scienze Pedagogiche e Filosofiche, University of Cagliari, Via Is Mirrionis 1, 09123, Cagliari, Italy

    Hector Freytes

  2. Instituto Argentino de Matemática (IAM), Saavedra 15-3er Piso, 1083, Buenos Aires, Argentina

    Hector Freytes

  3. CONICET, Buenos Aires, Argentina

    Hector Freytes

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  1. Hector Freytes
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Correspondence to Hector Freytes.

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The author express his gratitude to Roberto Cignoli, for his advice during the preparation of this paper.

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Freytes, H. Pavelka-style completeness in expansions of Łukasiewicz logic. Arch. Math. Logic 47, 15–23 (2008). https://doi.org/10.1007/s00153-008-0064-8

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  • DOI: https://doi.org/10.1007/s00153-008-0064-8

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