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States on semi-divisible residuated lattices

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Abstract

Given a residuated lattice L, we prove that the subset MV(L) of complement elements x * of L generates an MV-algebra if, and only if L is semi-divisible. Riečan states on a semi-divisible residuated lattice L, and Riečan states on MV(L) are essentially the very same thing. The same holds for Bosbach states as far as L is divisible. There are semi-divisible residuated lattices that do not have Bosbach states.

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Authors and Affiliations

  1. Tampere University of Technology, P.O. Box 553, 33101, Tampere, Finland

    Esko Turunen & Janne Mertanen

Authors
  1. Esko Turunen
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  2. Janne Mertanen
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Correspondence to Esko Turunen.

Additional information

These results were obtained when the authors visited Academy of Science, Czech Republic, Institute of Comp. Sciences in Autumn 2006.

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Turunen, E., Mertanen, J. States on semi-divisible residuated lattices. Soft Comput 12, 353–357 (2008). https://doi.org/10.1007/s00500-007-0182-y

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  • DOI: https://doi.org/10.1007/s00500-007-0182-y

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