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A Proof of Standard Completeness for Esteva and Godo's Logic MTL

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Abstract

In the present paper we show that any at most countable linearly-ordered commutative residuated lattice can be embedded into a commutative residuated lattice on the real unit interval [0, 1]. We use this result to show that Esteva and Godo's logic MTL is complete with respect to interpretations into commutative residuated lattices on [0, 1]. This solves an open problem raised in.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, University of Pécs, Ifjúság u. 6, H-7624, Pécs, Hungary

    Sándor Jenei

  2. Department of Mathematics, University of Siena, Via del Capitano 15, 53100, Siena, Italy

    Franco Montagna

Authors
  1. Sándor Jenei
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  2. Franco Montagna
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Jenei, S., Montagna, F. A Proof of Standard Completeness for Esteva and Godo's Logic MTL. Studia Logica 70, 183–192 (2002). https://doi.org/10.1023/A:1015122331293

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  • DOI: https://doi.org/10.1023/A:1015122331293

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