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States on semi-divisible residuated lattices
Authors:Esko Turunen  Janne Mertanen
Affiliation:(1) Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland
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. These results were obtained when the authors visited Academy of Science, Czech Republic, Institute of Comp. Sciences in Autumn 2006.
Keywords:Residuated lattice  Wajsberg algebra            MV-algebra  Probability theory
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