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Monadic GMV-algebras

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Abstract

Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. GMV-algebras are a non-commutative generalization of MV-algebras and are an algebraic counterpart of the non-commutative Łukasiewicz infinite valued logic. We introduce monadic GMV-algebras and describe their connections to certain couples of GMV-algebras and to left adjoint mappings of canonical embeddings of GMV-algebras. Furthermore, functional MGMV-algebras are studied and polyadic GMV-algebras are introduced and discussed.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Faculty of Sciences, Palacký University, Tomkova 40, 779 00, Olomouc, Czech Republic

    Jiří Rachůnek

  2. VŠB–Technical University Ostrava, Sokolská 33, 70121, Ostrava, Czech Republic

    Dana Šalounová

Authors
  1. Jiří Rachůnek
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  2. Dana Šalounová
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Correspondence to Jiří Rachůnek.

Additional information

The first author was supported by the Council of Czech Government, MSM 6198959214.

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Rachůnek, J., Šalounová, D. Monadic GMV-algebras. Arch. Math. Logic 47, 277–297 (2008). https://doi.org/10.1007/s00153-008-0086-2

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  • DOI: https://doi.org/10.1007/s00153-008-0086-2

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