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  1. A Common Generalization for MV-Algebras and Łukasiewicz–Moisil Algebras.George Georgescu & Andrei Popescu - 2006 - Archive for Mathematical Logic 45 (8):947-981.
    We introduce the notion of n-nuanced MV-algebra by performing a Łukasiewicz–Moisil nuancing construction on top of MV-algebras. These structures extend both MV-algebras and Łukasiewicz–Moisil algebras, thus unifying two important types of structures in the algebra of logic. On a logical level, n-nuanced MV-algebras amalgamate two distinct approaches to many valuedness: that of the infinitely valued Łukasiewicz logic, more related in spirit to the fuzzy approach, and that of Moisil n-nuanced logic, which is more concerned with nuances of truth rather than (...)
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  • Wajsberg Algebras and Post Algebras.Antonio Jesús Rodríguez & Antoni Torrens - 1994 - Studia Logica 53 (1):1 - 19.
    We give a presentation of Post algebras of ordern+1 (n1) asn+1 bounded Wajsberg algebras with an additional constant, and we show that a Wajsberg algebra admits a P-algebra reduct if and only if it isn+1 bounded.
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  • An Algebraic Approach to Elementary Theories Based on N‐Valued Lukasiewicz Logics.Roberto Cignoli - 1984 - Mathematical Logic Quarterly 30 (1‐6):87-96.
  • Łukasiewicz-Moisil Relation Algebras.Andrei Popescu - 2005 - Studia Logica 81 (2):167-189.
    We introduce Łukasiewicz-Moisil relation algebras, obtained by considering a relational dimension over Łukasiewicz-Moisil algebras. We prove some arithmetical properties, provide a characterization in terms of complex algebras, study the connection with relational Post algebras and characterize the simple structures and the matrix relation algebras.
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  • The Priestley Duality for Wajsberg Algebras.N. G. Martínez - 1990 - Studia Logica 49 (1):31 - 46.
    The Priestley duality for Wajsberg algebras is developed. The Wajsberg space is a De Morgan space endowed with a family of functions that are obtained in rather natural way.As a first application of this duality, a theorem about unicity of the structure is given.
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  • An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras.L. J. González, M. B. Lattanzi & A. G. Petrovich - 2017 - Logica Universalis 11 (4):439-463.
    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 \. 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 (...)
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  • Maximal Subalgebras of MVn-Algebras. A Proof of a Conjecture of A. Monteiro.Roberto Cignoli & Luiz Monteiro - 2006 - Studia Logica 84 (3):393-405.
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  • Maximal Subalgebras of MVn-Algebras. A Proof of a Conjecture of A. Monteiro.Roberto Cignoli & Luiz Monteiro - 2006 - Studia Logica 84 (3):393 - 405.
    For each integer n ≥ 2, MVn denotes the variety of MV-algebras generated by the MV-chain with n elements. Algebras in MVn are represented as continuous functions from a Boolean space into a n-element chain equipped with the discrete topology. Using these representations, maximal subalgebras of algebras in MVn are characterized, and it is shown that proper subalgebras are intersection of maximal subalgebras. When A ∈ MV3, the mentioned characterization of maximal subalgebras of A can be given in terms of (...)
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  • An Algebraic Approach to Elementary Theories Based Onn-Valued Lukasiewicz Logics.Roberto Cignoli - 1984 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (1-6):87-96.
  • Free Nilpotent Minimum Algebras.Manuela Busaniche - 2006 - Mathematical Logic Quarterly 52 (3):219-236.
    In the present paper we give a description of the free algebra over an arbitrary set of generators in the variety of nilpotent minimum algebras. Such description is given in terms of a weak Boolean product of directly indecomposable algebras over the Boolean space corresponding to the Boolean subalgebra of the free NM-algebra.
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