Archive for Mathematical Logic 45 (8):947-981 (2006)

Andrei Popescu
Politehnica University of Bucharest
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 truth degree. We study n-nuanced MV-algebras mainly from the algebraic and categorical points of view, and also consider some basic model-theoretic aspects. The relationship with a suitable notion of n-nuanced ordered group via an extension of the Γ construction is also analyzed
Keywords n-Nuanced MV-algebra  Łukasiewicz–Moisil algebra   n-Nuanced ordered group
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DOI 10.1007/s00153-006-0020-4
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Mathematical Logic.J. Donald Monk - 1976 - Springer Verlag.
Fuzzy Sets.Lofti A. Zadeh - 1965 - Information and Control 8 (1):338--53.
Model Theory.Gebhard Fuhrken - 1976 - Journal of Symbolic Logic 41 (3):697-699.

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