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George Georgescu [15]G. Georgescu [3]
  1. Lavinia Corina Ciungu, George Georgescu & Claudia Mureşan (2013). Generalized Bosbach States: Part II. [REVIEW] Archive for Mathematical Logic 52 (7-8):707-732.
    We continue the investigation of generalized Bosbach states that we began in Part I, restricting our research to the commutative case and treating further aspects related to these states. Part II is concerned with similarity convergences, continuity of states and the construction of the s-completion of a commutative residuated lattice, where s is a generalized Bosbach state.
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  2. Lavinia Corina Ciungu, George Georgescu & Claudia Mureşan (2013). Generalized Bosbach States: Part I. [REVIEW] Archive for Mathematical Logic 52 (3-4):335-376.
    States have been introduced on commutative and non-commutative algebras of fuzzy logics as functions defined on these algebras with values in [0,1]. Starting from the observation that in the definition of Bosbach states there intervenes the standard MV-algebra structure of [0,1], in this paper we introduce Bosbach states defined on residuated lattices with values in residuated lattices. We are led to two types of generalized Bosbach states, with distinct behaviours. Properties of generalized states are useful for the development of an (...)
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  3. George Georgescu & Denisa Diaconescu (2011). Forcing Operators on MTL-Algebras. Mathematical Logic Quarterly 57 (1):47-64.
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  4. George Georgescu (2010). States on Polyadic Mv-Algebras. Studia Logica 94 (2):231 - 243.
    This paper is a contribution to the algebraic logic of probabilistic models of Łukasiewicz predicate logic. We study the MV-states defined on polyadic MV-algebras and prove an algebraic many-valued version of Gaifman’s completeness theorem.
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  5. Antonio Di Nola, George Georgescu & Luca Spada (2008). Forcing in Łukasiewicz Predicate Logic. Studia Logica 89 (1):111-145.
    In this paper we study the notion of forcing for Łukasiewicz predicate logic (Ł∀, for short), along the lines of Robinson’s forcing in classical model theory. We deal with both finite and infinite forcing. As regard to the former we prove a Generic Model Theorem for Ł∀, while for the latter, we study the generic and existentially complete standard models of Ł∀.
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  6. George Georgescu (2008). Fuzzy Power Structures. Archive for Mathematical Logic 47 (3):233-261.
    Power structures are obtained by lifting some mathematical structure (operations, relations, etc.) from an universe X to its power set ${\mathcal{P}(X)}$ . A similar construction provides fuzzy power structures: operations and fuzzy relations on X are extended to operations and fuzzy relations on the set ${\mathcal{F}(X)}$ of fuzzy subsets of X. In this paper we study how this construction preserves some properties of fuzzy sets and fuzzy relations (similarity, congruence, etc.). We define the notions of good, very good, Hoare good (...)
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  7. I. C. Baianu, R. Brown, G. Georgescu & J. F. Glazebrook (2006). Complex Non-Linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks. [REVIEW] Axiomathes 16 (1-2):65-122.
    A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil (...)
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  8. George Georgescu (2006). N-Valued Logics and Łukasiewicz–Moisil Algebras. Axiomathes 16 (1-2):123-136.
    Fundamental properties of N-valued logics are compared and eleven theorems are presented for their Logic Algebras, including Łukasiewicz–Moisil Logic Algebras represented in terms of categories and functors. For example, the Fundamental Logic Adjunction Theorem allows one to transfer certain universal, or global, properties of the Category of Boolean Algebras.
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  9. George Georgescu & Andrei Popescu (2006). A Common Generalization for MV-Algebras and Łukasiewicz–Moisil Algebras. 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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  10. G. Georgescu (2005). Georgescu, G. 2006, N-Valued Logics and Lukasiewicz-Moisil Algebras, Axiomathes, 16 (1-2): 123-136. N–Valued Logics and Lukasiewicz–Moisil Algebras. [REVIEW] Axiomathes 16 (1-2).
     
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  11. George Georgescu & Andrei Popescu (2004). Non-Dual Fuzzy Connections. Archive for Mathematical Logic 43 (8):1009-1039.
    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 ones (like, for instance, conjugated pair), that (...)
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  12. D. Dragulici & G. Georgescu (2001). Algebraic Logic for Rational Pavelka Predicate Calculus. Mathematical Logic Quarterly 47 (3):315-326.
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  13. Lawrence P. Belluce, Antonio Di Nola & George Georgescu (1999). PerfectMV-Algebras Andl-Rings. Journal of Applied Non-Classical Logics 9 (1):159-172.
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  14. George Georgescu (1991). F‐Multipliers and the Localization of Distributive Lattices II. Mathematical Logic Quarterly 37 (19‐22):293-300.
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  15. George Georgescu & Iana Voiculescu (1985). Eastern Model‐Theory for Boolean‐Valued Theories. Mathematical Logic Quarterly 31 (1‐6):79-88.
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  16. George Georgescu (1983). Chang's Modal Operators in Algebraic Logic. Studia Logica 42 (1):43 - 48.
    Chang algebras as algebraic models for Chang's modal logics [1] are defined. The main result of the paper is a representation theorem for these algebras.
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  17. George Georgescu (1982). Algebraic Analysis of the Topological Logic L(I). Mathematical Logic Quarterly 28 (27‐32):447-454.
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