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Rivieccio, Umberto

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0000-0003-1364-5003
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Rivieccio
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Umberto
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2014 - 201922020 - 20211
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Autor: Jansana, Ramon × Tiene archivos: true ×

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Mostrando 1 - 3 de 3
  • Miniatura
    Publicación
    Dualities for modal N4-lattices
    (Oxford University Press, 2014-08) Jansana, Ramon; Rivieccio, Umberto
    We introduce a new Priestley-style topological duality for N4-lattices, which are the algebraic counterpart of paraconsistent Nelson logic. Our duality differs from the existing one, due to S. Odintsov, in that we only rely on Esakia duality for Heyting algebras and not on the duality for De Morgan algebras of Cornish and Fowler. A major advantage of our approach is that we obtain a simple description for our topological structures, which allows us to extend the duality to other algebraic structures such as N4-lattices with monotonic modal operators, and also to provide a neighbourhood semantics for the non-normal modal logic corresponding to these algebras.
  • Miniatura
    Publicación
    Four-valued modal logic: Kripke semantics and duality
    (IEEE Xplore, 2017-02) Rivieccio, Umberto; Jung, Achim; Jansana, Ramon
    We introduce a family of modal expansions of Belnap–Dunn four-valued logic and related systems, and interpret them in many-valued Kripke structures. Using algebraic logic techniques and topological duality for modal algebras, and generalizing the so-called twist-structure representation, we axiomatize by means of Hilbert-style calculi the least modal logic over the four-element Belnap lattice and some of its axiomatic extensions. We study the algebraic models of these systems, relating them to the algebraic semantics of classical multi-modal logic. This link allows us to prove that both local and global consequence of the least four-valued modal logic enjoy the finite model property and are therefore decidable.
  • Miniatura
    Publicación
    Quasi-Nelson algebras and fragments
    (Cambridge University Press, 2021-05-11) Rivieccio, Umberto; Jansana, Ramon
    The variety of quasi-Nelson algebras (QNAs) has been recently introduced and characterised in several equivalent ways: among others, as (1) the class of bounded commutative integral (but non-necessarily involutive) residuated lattices satisfying the Nelson identity, as well as (2) the class of (0, 1)-congruence orderable commutative integral residuated lattices. Logically, QNAs are the algebraic counterpart of quasi-Nelson logic, which is the (algebraisable) extension of the substructural logic ℱℒew (Full Lambek calculus with Exchange and Weakening) by the Nelson axiom. In the present paper, we collect virtually all the results that are currently known on QNAs, including solutions to certain questions left open in earlier publications. Furthermore, we extend our study to some subreducts of QNAs, that is, classes of algebras corresponding to fragments of the algebraic language obtained by eliding either the implication or the lattice operations.