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On involutive FL e -monoids

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Abstract

The paper deals with involutive FL e -monoids, that is, commutative residuated, partially-ordered monoids with an involutive negation. Involutive FL e -monoids over lattices are exactly involutive FL e -algebras, the algebraic counterparts of the substructural logic IUL. A cone representation is given for conic involutive FL e -monoids, along with a new construction method, called twin-rotation. Some classes of finite involutive FL e -chains are classified by using the notion of rank of involutive FL e -chains, and a kind of duality is developed between positive and non-positive rank algebras. As a side effect, it is shown that the substructural logic IUL plus t ↔ f does not have the finite model property.

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Authors and Affiliations

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

    Sándor Jenei

  2. Institute for Discrete Mathematics and Geometry, Technical University of Vienna, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    Sándor Jenei

  3. Research Center for Integrated Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan

    Hiroakira Ono

Authors
  1. Sándor Jenei
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  2. Hiroakira Ono
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Correspondence to Sándor Jenei.

Additional information

This work was supported by the EC MC grant 219376, the OMFB-00733/2008 research grant, and the OTKA-76811 grant.

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Jenei, S., Ono, H. On involutive FL e -monoids. Arch. Math. Logic 51, 719–738 (2012). https://doi.org/10.1007/s00153-012-0295-6

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  • DOI: https://doi.org/10.1007/s00153-012-0295-6

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