19 found
Order:
  1.  59
    N-Valued Logics and Łukasiewicz–Moisil Algebras.George Georgescu - 2006 - 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.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  2.  32
    States on Polyadic MV-Algebras.George Georgescu - 2010 - 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.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  3.  16
    Non-Dual Fuzzy Connections.George Georgescu & Andrei Popescu - 2004 - 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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  4.  3
    Algebraic Logic for Rational Pavelka Predicate Calculus.Daniel Drăgulici & George Georgescu - 2001 - Mathematical Logic Quarterly 47 (3):315-326.
    In this paper we define the polyadic Pavelka algebras as algebraic structures for Rational Pavelka predicate calculus . We prove two representation theorems which are the algebraic counterpart of the completness theorem for RPL∀.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  5.  23
    Forcing in Łukasiewicz Predicate Logic.Antonio Di Nola, George Georgescu & Luca Spada - 2008 - 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∀.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  6.  16
    F-Multipliers and the Localization of Distributive Lattices II.George Georgescu - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (19-22):293-300.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  7.  16
    Eastern Model-Theory for Boolean-Valued Theories.George Georgescu & Iana Voiculescu - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (1-6):79-88.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  8.  15
    Algebraic Analysis of the Topological Logic L.George Georgescu - 1982 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 28 (27-32):447-454.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  9.  14
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  10.  9
    PerfectMV-Algebras Andl-Rings.Lawrence P. Belluce, Antonio Di Nola & George Georgescu - 1999 - Journal of Applied Non-Classical Logics 9 (1):159-172.
  11.  12
    Fuzzy Power Structures.George Georgescu - 2008 - 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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  12.  8
    Generalized Bosbach States: Part I. [REVIEW]Lavinia Corina Ciungu, George Georgescu & Claudia Mureşan - 2013 - 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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  13.  17
    Chang's Modal Operators in Algebraic Logic.George Georgescu - 1983 - 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.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  14.  6
    Forcing Operators on MTL-Algebras.George Georgescu & Denisa Diaconescu - 2011 - Mathematical Logic Quarterly 57 (1):47-64.
    We study the forcing operators on MTL-algebras, an algebraic notion inspired by the Kripke semantics of the monoidal t -norm based logic . At logical level, they provide the notion of the forcing value of an MTL-formula. We characterize the forcing operators in terms of some MTL-algebras morphisms. From this result we derive the equality of the forcing value and the truth value of an MTL-formula.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  15.  6
    F‐Multipliers and the Localization of Distributive Lattices II.George Georgescu - 1991 - Mathematical Logic Quarterly 37 (19‐22):293-300.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  16.  5
    Algebraic Analysis of the Topological Logic L(I).George Georgescu - 1982 - Mathematical Logic Quarterly 28 (27‐32):447-454.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  17.  4
    Generalized Bosbach States: Part II. [REVIEW]Lavinia Corina Ciungu, George Georgescu & Claudia Mureşan - 2013 - 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.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  18.  2
    Factor Congruence Lifting Property.George Georgescu & Claudia Mureşan - 2017 - Studia Logica 105 (1):179-216.
    In previous work, we have introduced and studied a lifting property in congruence–distributive universal algebras which we have defined based on the Boolean congruences of such algebras, and which we have called the Congruence Boolean Lifting Property. In a similar way, a lifting property based on factor congruences can be defined in congruence–distributive algebras; in this paper we introduce and study this property, which we have called the Factor Congruence Lifting Property. We also define the Boolean Lifting Property in varieties (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  19.  4
    Eastern Model‐Theory for Boolean‐Valued Theories.George Georgescu & Iana Voiculescu - 1985 - Mathematical Logic Quarterly 31 (1‐6):79-88.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography