•  24
    Łukasiewicz-Moisil Relation Algebras
    Studia Logica 81 (2): 167-189. 2005.
    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.
  •  2
    Similarity Convergence in Residuated Structures
    with George Georgescu
    Logic Journal of the IGPL 13 (4): 389-413. 2005.
    We introduce and study a notion of logical convergence in residuated lattices . It is considered a convergence in similarity degree, rather than a bare order convergence – the lack of symmetry of residuated lattices brings our approach more related to the logical structure than to the set of truth values
  •  47
    An Institution-Independent Proof of the Robinson Consistency Theorem
    with Daniel Gâinâ
    Studia Logica 85 (1): 41-73. 2007.
    We prove an institutional version of A. Robinson ’s Consistency Theorem. This result is then appliedto the institution of many-sorted first-order predicate logic and to two of its variations, infinitary and partial, obtaining very general syntactic criteria sufficient for a signature square in order to satisfy the Robinson consistency and Craig interpolation properties
  •  21
    A common generalization for MV-algebras and Łukasiewicz–Moisil algebras
    with George Georgescu
    Archive for Mathematical Logic 45 (8): 947-981. 2006.
    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 logi…Read more
  •  28
    A general approach to fuzzy concepts
    Mathematical Logic Quarterly 50 (3): 265-280. 2004.
    The paper proposes a flexible way to build concepts within fuzzy logic and set theory. The framework is general enough to capture some important particular cases, with their own independent interpretations, like “antitone” or “isotone” concepts constructed from fuzzy binary relations, but also to allow the two universes to be equipped each with its own truth structure. Perhaps the most important feature of our approach is that we do not commit ourselves to any kind of logical connector, covering…Read more
  •  31
    Non-dual fuzzy connections
    with George Georgescu
    Archive for Mathematical Logic 43 (8): 1009-1039. 2004.
    The lack of double negation and de Morgan properties makes fuzzy logic unsymmetrical. This is the reason why fuzzy versions of notions like closure operator or Galois connection deserve attention for both antiotone and isotone cases, these two cases not being dual. This paper offers them attention, comming to the following conclusions: – some kind of hardly describable ‘‘local preduality’’ still makes possible important parallel results; – interesting new concepts besides antitone and isotone on…Read more