8 found
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  1.  10
    Twist Structures and Nelson Conuclei.Manuela Busaniche, Nikolaos Galatos & Miguel Andrés Marcos - 2022 - Studia Logica 110 (4):949-987.
    Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common generalization of them. Nelson conucleus algebras unify these examples and further extend them to the non-commutative setting. We study their structure, establish a representation theorem for them in terms of twist structures and conuclei that results in a categorical adjunction, and explore situations where the representation is actually an isomorphism. In the latter case, the adjunction is elevated to a categorical equivalence. By (...)
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  2.  18
    Free nilpotent minimum algebras.Manuela Busaniche - 2006 - Mathematical Logic Quarterly 52 (3):219-236.
    In the present paper we give a description of the free algebra over an arbitrary set of generators in the variety of nilpotent minimum algebras. Such description is given in terms of a weak Boolean product of directly indecomposable algebras over the Boolean space corresponding to the Boolean subalgebra of the free NM-algebra.
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  3.  22
    Geometry of Robinson consistency in Łukasiewicz logic.Manuela Busaniche & Daniele Mundici - 2007 - Annals of Pure and Applied Logic 147 (1):1-22.
    We establish the Robinson joint consistency theorem for the infinite-valued propositional logic of Łukasiewicz. As a corollary we easily obtain the amalgamation property for MV-algebras—the algebras of Łukasiewicz logic: all pre-existing proofs of this latter result make essential use of the Pierce amalgamation theorem for abelian lattice-ordered groups together with the categorical equivalence Γ between these groups and MV-algebras. Our main tools are elementary and geometric.
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  4.  9
    Poset Product and BL-Chains.Manuela Busaniche & Conrado Gomez - 2018 - Studia Logica 106 (4):739-756.
    Different constructions of BL-chains are compared. We establish when the ordinal sum and the poset product of the same family of BL-chains coincide. We also compare the poset product of MV-chains and product chains with saturated BL-chains.
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  5.  3
    Nelson Conuclei and Nuclei: The Twist Construction Beyond Involutivity.Umberto Rivieccio & Manuela Busaniche - forthcoming - Studia Logica:1-39.
    Recent work by Busaniche, Galatos and Marcos introduced a very general twist construction, based on the notion of _conucleus_, which subsumes most existing approaches. In the present paper we extend this framework one step further, so as to allow us to construct and represent algebras which possess a negation that is not necessarily involutive. Our aim is to capture the main properties of the largest class that admits such a representation, as well as to be able to recover the well-known (...)
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  6.  32
    A Categorical Equivalence for Stonean Residuated Lattices.Manuela Busaniche, Roberto Cignoli & Miguel Andrés Marcos - 2019 - Studia Logica 107 (2):399-421.
    We follow the ideas given by Chen and Grätzer to represent Stone algebras and adapt them for the case of Stonean residuated lattices. Given a Stonean residuated lattice, we consider the triple formed by its Boolean skeleton, its algebra of dense elements and a connecting map. We define a category whose objects are these triples and suitably defined morphisms, and prove that we have a categorical equivalence between this category and that of Stonean residuated lattices. We compare our results with (...)
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  7.  12
    Functional representation of finitely generated free algebras in subvarieties of BL-algebras.Manuela Busaniche, José Luis Castiglioni & Noemí Lubomirsky - 2020 - Annals of Pure and Applied Logic 171 (2):102757.
    Consider any subvariety of BL-algebras generated by a single BL-chain which is the ordinal sum of the standard MV-algebra on [0, 1] and a basic hoop H. We present a geometrical characterization of elements in the finitely generated free algebra of each of these subvarieties. In this characterization there is a clear insight of the role of the regular and dense elements of the generating chain. As an application, we analyze maximal and prime filters in the free algebra.
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  8.  33
    Remarks on an algebraic semantics for paraconsistent Nelson's logic.Manuela Busaniche & Roberto Cignoli - 2011 - Manuscrito 34 (1):99-114.
    In the paper Busaniche and Cignoli we presented a quasivariety of commutative residuated lattices, called NPc-lattices, that serves as an algebraic semantics for paraconsistent Nelson’s logic. In the present paper we show that NPc-lattices form a subvariety of the variety of commutative residuated lattices, we study congruences of NPc-lattices and some subvarieties of NPc-lattices.
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