19 found
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  1.  24
    On Monadic MV-Algebras.Antonio Di Nola & Revaz Grigolia - 2004 - Annals of Pure and Applied Logic 128 (1-3):125-139.
    We define and study monadic MV-algebras as pairs of MV-algebras one of which is a special case of relatively complete subalgebra named m-relatively complete. An m-relatively complete subalgebra determines a unique monadic operator. A necessary and sufficient condition is given for a subalgebra to be m-relatively complete. A description of the free cyclic monadic MV-algebra is also given.
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  2.  28
    Perfect MV-Algebras Are Categorically Equivalent to Abelianl-Groups.Antonio Di Nola & Ada Lettieri - 1994 - Studia Logica 53 (3):417-432.
    In this paper we prove that the category of abelianl-groups is equivalent to the category of perfect MV-algebras. Furthermore, we give a finite equational axiomatization of the variety generated by perfect MV-algebras.
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  3.  32
    State-Morphism MV-Algebras.Antonio Di Nola & Anatolij Dvurečenskij - 2010 - Annals of Pure and Applied Logic 161 (2):161-173.
    We present a stronger variation of state MV-algebras, recently presented by T. Flaminio and F. Montagna, which we call state-morphism MV-algebras. Such structures are MV-algebras with an internal notion, a state-morphism operator. We describe the categorical equivalences of such state MV-algebras with the category of unital Abelian ℓ-groups with a fixed state operator and present their basic properties. In addition, in contrast to state MV-algebras, we are able to describe all subdirectly irreducible state-morphism MV-algebras.
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  4.  37
    Finitely Generated Free MV-Algebras and Their Automorphism Groups.Antonio Di Nola, Revaz Grigolia & Giovanni Panti - 1998 - Studia Logica 61 (1):65-78.
    The MV-algebra S m w is obtained from the (m+1)-valued ukasiewicz chain by adding infinitesimals, in the same way as Chang's algebra is obtained from the two-valued chain. These algebras were introduced by Komori in his study of varieties of MV-algebras. In this paper we describe the finitely generated totally ordered algebras in the variety MV m w generated by S m w . This yields an easy description of the free MV m w -algebras over one generator. We characterize (...)
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  5.  22
    An Analysis of the Logic of Riesz Spaces with Strong Unit.Antonio Di Nola, Serafina Lapenta & Ioana Leuştean - 2018 - Annals of Pure and Applied Logic 169 (3):216-234.
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  6.  26
    Compact Representations of BL-Algebras.Antonio Di Nola & Laurentiu Leustean - 2003 - Archive for Mathematical Logic 42 (8):737-761.
    In this paper we define sheaf spaces of BL-algebras (or BL-sheaf spaces), we study completely regular and compact BL-sheaf spaces and compact representations of BL-algebras and, finally, we prove that the category of non-trivial BL-algebras is equivalent with the category of compact local BL-sheaf spaces.
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  7.  20
    Natural Dualities for Varieties of BL-Algebras.Antonio Di Nola & Philippe Niederkorn - 2005 - Archive for Mathematical Logic 44 (8):995-1007.
    BL-algebras are the Lindenbaum algebras for Hájek's Basic Logic, just as Boolean algebras correspond to the classical propositional calculus. The finite totally ordered BL-algebras are ordinal sums of MV-chains. We develop a natural duality, in the sense of Davey and Werner, for each subvariety generated by a finite BL-chain, and we use it to describe the injective and the weak injective members of these classes.
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  8.  20
    Subvarieties of BL-Algebras Generated by Single-Component Chains.Antonio Di Nola, Francesc Esteva, Pere Garcia, Lluís Godo & Salvatore Sessa - 2002 - Archive for Mathematical Logic 41 (7):673-685.
    In this paper we study and equationally characterize the subvarieties of BL, the variety of BL-algebras, which are generated by families of single-component BL-chains, i.e. MV-chains, Product-chain or Gödel-chains. Moreover, it is proved that they form a segment of the lattice of subvarieties of BL which is bounded by the Boolean variety and the variety generated by all single-component chains, called ŁΠG.
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  9.  11
    Gödel Spaces and Perfect MV-Algebras.Antonio Di Nola & Revaz Grigolia - 2015 - Journal of Applied Logic 13 (3):270-284.
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  10.  32
    Algebraically Closed MV-Algebras and Their Sheaf Representation.Antonio Di Nola, Anna R. Ferraioli & Giacomo Lenzi - 2013 - Annals of Pure and Applied Logic 164 (3):349-355.
    In this paper we first provide a new axiomatization of algebraically closed MV-algebras based on McNaughtonʼs Theorem. Then we turn to sheaves, and we represent algebraically closed MV-algebras as algebras of global sections of sheaves, where the stalks are divisible MV-chains and the base space is Stonean.
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  11.  6
    An Approach to Stochastic Processes Via Non-Classical Logic.Antonio Di Nola, Anatolij Dvurečenskij & Serafina Lapenta - 2021 - Annals of Pure and Applied Logic 172 (9):103012.
  12.  18
    Erratum to “State-Morphism MV-Algebras” [Ann. Pure Appl. Logic 161 (2009) 161–173].Antonio Di Nola, A. Dvurečenskij & Ada Lettieri - 2010 - Annals of Pure and Applied Logic 161 (12):1605-1607.
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  13.  41
    A Discrete Representation of Free MV-Algebras.Antonio Di Nola, Revaz Grigolia & Luca Spada - 2010 - Mathematical Logic Quarterly 56 (3):279-288.
    We prove that the m -generated free MV-algebra is isomorphic to a quotient of the disjoint union of all the m -generated free MV-algebras. Such a quotient can be seen as the direct limit of a system consisting of all free MV-algebras and special maps between them as morphisms.
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  14.  44
    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∀.
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  15. Fuzziness in Italy – Traces of a Scattered History.Gianpiero Cattaneo, Giulianella Coletti, Antonio Di Nola, Mario Fedrizzi, Giangiacomo Gerla, Gabriella Pasi, Marco Elio Tabacchi, Settimo Termini & Aldo Ventre - 2017 - Archives for the Philosophy and History of Soft Computing 2017 (1).
    The history of Fuzziness in Italy is varied and scattered among a num- ber of research groups. As a matter of fact, “fuzziness” spread in Italy through a sort of spontaneous diffusion, and, also subsequently, no one felt the need to cre- ate some “national” common structure like an Association or similar things. Since a cohesive retelling would be next to impossible, a few members of the Italian fuzzy community have been asked to recount their experience and express their hopes (...)
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  16.  27
    Representation of MV-Algebras by Regular Ultrapowers of [0, 1].Antonio Di Nola, Giacomo Lenzi & Luca Spada - 2010 - Archive for Mathematical Logic 49 (4):491-500.
    We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0,1]. This result also implies the existence, for any cardinal α, of a single MV-algebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction with iterated ultrapowers, we show how to construct such an algebra of values in a definable (...)
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  17.  13
    Perfect MV-Algebras and L-Rings.Lawrence P. Belluce, Antonio Di Nola & George Georgescu - 1999 - Journal of Applied Non-Classical Logics 9 (1):159-172.
    ABSTRACT In this paper we shall prove that l-rings are categorally equivalent to the MV*-algebras, a subcategory of perfect MV-algebras. We shall use this equivalence in order to characterize l-rings as quotients of certain semirings of matrices over MV*-algebras. We shall establish a relation between l-ideals in l-rings and some ideals in MV*-algebras. This edlows us to study the MV* f-algebras, a subclass of the MV*-algebras corresponding to the f-rings.
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  18.  18
    A Discrete Free MV-Algebra Over One Generator.Antonio Di Nola & Brunella Gerla - 2001 - Journal of Applied Non-Classical Logics 11 (3-4):331-339.
    In this paper we give a representation of the free MV-algebra over one generator as a structure of functions having finite domain.
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  19.  1
    Duality Theory and Skeleta for Semisimple MV-Algebras.Antonio Di Nola & Giacomo Lenzi - 2018 - Studia Logica 106 (6):1239-1260.
    We start from Marra–Spada duality between semisimple MV-algebras and Tychonoff spaces, and we consider the particular cases when the \-skeleta of the MV-algebras are restricted in some way. In particular we consider antiskeletal MV-algebras, that is, the ones whose \-skeleton is trivial.
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