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.
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This work was partially supported by Universidad Nacional de La Pampa (Fac. de Cs. Exactas y Naturales) under the Grant P.I. 64 M, Res. 432/14 CD.
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González, L.J., Lattanzi, M.B. & Petrovich, A.G. An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras. Log. Univers. 11, 439–463 (2017). https://doi.org/10.1007/s11787-017-0181-4
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DOI: https://doi.org/10.1007/s11787-017-0181-4