15 found
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  1.  61
    Nothing but the Truth.Andreas Pietz & Umberto Rivieccio - 2013 - Journal of Philosophical Logic 42 (1):125-135.
    A curious feature of Belnap’s “useful four-valued logic”, also known as first-degree entailment (FDE), is that the overdetermined value B (both true and false) is treated as a designated value. Although there are good theoretical reasons for this, it seems prima facie more plausible to have only one of the four values designated, namely T (exactly true). This paper follows this route and investigates the resulting logic, which we call Exactly True Logic.
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  2.  12
    An Algebraic View of Super-Belnap Logics.Hugo Albuquerque, Adam Přenosil & Umberto Rivieccio - 2017 - Studia Logica 105 (6):1051-1086.
    The Belnap–Dunn logic is a well-known and well-studied four-valued logic, but until recently little has been known about its extensions, i.e. stronger logics in the same language, called super-Belnap logics here. We give an overview of several results on these logics which have been proved in recent works by Přenosil and Rivieccio. We present Hilbert-style axiomatizations, describe reduced matrix models, and give a description of the lattice of super-Belnap logics and its connections with graph theory. We adopt the point of (...)
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  3.  25
    An Infinity of Super-Belnap Logics.Umberto Rivieccio - 2012 - Journal of Applied Non-Classical Logics 22 (4):319 - 335.
    We look at extensions (i.e., stronger logics in the same language) of the Belnap?Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap?Dunn and do not coincide with any of the known extensions (Kleene?s logics, Priest?s logic of paradox). We characterise the reduced algebraic models of these new logics and prove a completeness result for the first and last element of the chain stating that both logics are determined by a single finite logical (...)
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  4.  13
    The Logic of Distributive Bilattices.Félix Bou & Umberto Rivieccio - 2011 - Logic Journal of the IGPL 19 (1):183-216.
    Bilattices, introduced by Ginsberg as a uniform framework for inference in artificial intelligence, are algebraic structures that proved useful in many fields. In recent years, Arieli and Avron developed a logical system based on a class of bilattice-based matrices, called logical bilattices, and provided a Gentzen-style calculus for it. This logic is essentially an expansion of the well-known Belnap–Dunn four-valued logic to the standard language of bilattices. Our aim is to study Arieli and Avron’s logic from the perspective of abstract (...)
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  5.  13
    Bilattice Logic of Epistemic Actions and Knowledge.Zeinab Bakhtiari, Hans van Ditmarsch & Umberto Rivieccio - 2020 - Annals of Pure and Applied Logic 171 (6):102790.
    Baltag, Moss, and Solecki proposed an expansion of classical modal logic, called logic of epistemic actions and knowledge (EAK), in which one can reason about knowledge and change of knowledge. Kurz and Palmigiano showed how duality theory provides a flexible framework for modeling such epistemic changes, allowing one to develop dynamic epistemic logics on a weaker propositional basis than classical logic (for example an intuitionistic basis). In this paper we show how the techniques of Kurz and Palmigiano can be further (...)
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  6.  5
    Representation of Interlaced Trilattices.Umberto Rivieccio - 2013 - Journal of Applied Logic 11 (2):174-189.
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  7.  14
    Bilattices with Implications.Félix Bou & Umberto Rivieccio - 2013 - Studia Logica 101 (4):651-675.
    In a previous work we studied, from the perspective ofAlgebraic Logic, the implicationless fragment of a logic introduced by O. Arieli and A. Avron using a class of bilattice-based logical matrices called logical bilattices. Here we complete this study by considering the Arieli-Avron logic in the full language, obtained by adding two implication connectives to the standard bilattice language. We prove that this logic is algebraizable and investigate its algebraic models, which turn out to be distributive bilattices with additional implication (...)
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  8.  6
    Locally Tabular $$Ne $$ Locally Finite.Sérgio Marcelino & Umberto Rivieccio - 2017 - Logica Universalis 11 (3):383-400.
    We show that for an arbitrary logic being locally tabular is a strictly weaker property than being locally finite. We describe our hunt for a logic that allows us to separate the two properties, revealing weaker and weaker conditions under which they must coincide, and showing how they are intertwined. We single out several classes of logics where the two notions coincide, including logics that are determined by a finite set of finite matrices, selfextensional logics, algebraizable and equivalential logics. Furthermore, (...)
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  9.  5
    Bilattice Public Announcement Logic.Umberto Rivieccio - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 459-477.
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  10.  3
    Nelson’s Logic ????Thiago Nascimento, Umberto Rivieccio, João Marcos & Matthew Spinks - 2020 - Logic Journal of the IGPL 28 (6):1182-1206.
    Besides the better-known Nelson logic and paraconsistent Nelson logic, in 1959 David Nelson introduced, with motivations of realizability and constructibility, a logic called $\mathcal{S}$. The logic $\mathcal{S}$ was originally presented by means of a calculus with infinitely many rule schemata and no semantics. We look here at the propositional fragment of $\mathcal{S}$, showing that it is algebraizable, in the sense of Blok and Pigozzi, with respect to a variety of three-potent involutive residuated lattices. We thus introduce the first known algebraic (...)
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  11.  1
    Fragments of Quasi-Nelson: The Algebraizable Core.Umberto Rivieccio - forthcoming - Logic Journal of the IGPL.
    This is the second of a series of papers that investigate fragments of quasi-Nelson logic from an algebraic logic standpoint. QNL, recently introduced as a common generalization of intuitionistic and Nelson’s constructive logic with strong negation, is the axiomatic extension of the substructural logic $FL_{ew}$ by the Nelson axiom. The algebraic counterpart of QNL is a class of commutative integral residuated lattices that includes both Heyting and Nelson algebras and can be characterized algebraically in several alternative ways. The present paper (...)
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  12. Logiche polivalenti per l'Intelligenza Artificiale: il sistema di Ginsberg.Umberto Rivieccio - 2005 - Epistemologia 28 (1):25-44.
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  13.  7
    Multivalued Logics for Artificial Intelligence: Ginsberg's System.Umberto Rivieccio - 2005 - Epistemologia 28 (1).
  14.  3
    Non-Involutive Twist-Structures.Umberto Rivieccio, Paulo Maia & Achim Jung - 2020 - Logic Journal of the IGPL 28 (5):973-999.
    A recent paper by Jakl, Jung and Pultr succeeded for the first time in establishing a very natural link between bilattice logic and the duality theory of d-frames and bitopological spaces. In this paper we further exploit, extend and investigate this link from an algebraic and a logical point of view. In particular, we introduce classes of algebras that extend bilattices, d-frames and N4-lattices to a setting in which the negation is not necessarily involutive, and we study corresponding logics. We (...)
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  15. What is Abstract Algebraic Logic?Umberto Rivieccio - 2009 - Epistemologia 32 (2):255.