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Logica Universalis

, Volume 11, Issue 4, pp 439–463 | Cite as

An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras

  • L. J. González
  • M. B. Lattanzi
  • A. G. Petrovich
Article
  • 32 Downloads

Abstract

An alternative notion of an existential quantifier on four-valued Łukasiewicz algebras is introduced. The class of four-valued Łukasiewicz algebras endowed with this existential quantifier determines a variety which is denoted by \(\mathbb {M}_{\frac{2}{3}}\mathbb {L}_4\). It is shown that the alternative existential quantifier is interdefinable with the standard existential quantifier on a four-valued Łukasiewicz algebra. Some connections between the new existential quantifier and the existential quantifiers defined on bounded distributive lattices and Boolean algebras are given. Finally, a completeness theorem for the monadic four-valued Łukasiewicz predicate calculus corresponding to the dual of the alternative existential quantifier is proven.

Keywords

Four-valued Łukasiewicz algebras quantifiers monadic logics 

Mathematics Subject Classification

Primary 03B50 Secondary 06D30 06D35 06D20 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • L. J. González
    • 1
  • M. B. Lattanzi
    • 1
  • A. G. Petrovich
    • 2
  1. 1.Facultad de Ciencias Exactas y NaturalesUniversidad Nacional de La PampaSanta RosaArgentina
  2. 2.Departamento de Matemática, Facultad de Ciencias Exactas y NaturalesUniversidad Nacional de Buenos AiresPabellón I - Ciudad UniversitariaArgentina

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