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A Gentzen system for involutive residuated lattices

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Abstract.

We establish a cut-free Gentzen system for involutive residuated lattices and provide an algebraic proof of completeness. As a result we conclude that the equational theory of involutive residuated lattices is decidable. The connection to noncommutative linear logic is outlined.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289, Darmstadt, Germany

    Annika M. Wille

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  1. Annika M. Wille
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Correspondence to Annika M. Wille.

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Received July 22, 2004; accepted in final form July 19, 2005.

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Wille, A.M. A Gentzen system for involutive residuated lattices. Algebra univers. 54, 449–463 (2005). https://doi.org/10.1007/s00012-005-1957-6

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  • DOI: https://doi.org/10.1007/s00012-005-1957-6

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