Archive for Mathematical Logic

, Volume 45, Issue 8, pp 947–981 | Cite as

A common generalization for MV-algebras and Łukasiewicz–Moisil algebras

  • George Georgescu
  • Andrei Popescu


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.


n-Nuanced MV-algebra Łukasiewicz–Moisil algebra n-Nuanced ordered group 

Mathematics Subject Classification (2000)

06D35 03G20 06F15 


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of BucharestBucharestRomania
  2. 2.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania
  3. 3.Deparment of Computer ScienceUniversity of Illinois at Urbana-ChampaignChampaignUSA

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