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Umberto Rivieccio [27]U. Rivieccio [4]
  1.  86
    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.  99
    Intuitionistic Modal Algebras.Sergio A. Celani & Umberto Rivieccio - forthcoming - Studia Logica:1-50.
    Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations (...)
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  3.  99
    Fragments of quasi-Nelson: residuation.U. Rivieccio - 2023 - Journal of Applied Non-Classical Logics 33 (1):52-119.
    Quasi-Nelson logic (QNL) was recently introduced as a common generalisation of intuitionistic logic and Nelson's constructive logic with strong negation. Viewed as a substructural logic, QNL is the axiomatic extension of the Full Lambek Calculus with Exchange and Weakening by the Nelson axiom, and its algebraic counterpart is a variety of residuated lattices called quasi-Nelson algebras. Nelson's logic, in turn, may be obtained as the axiomatic extension of QNL by the double negation (or involutivity) axiom, and intuitionistic logic as the (...)
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  4. 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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  5. The Value of the One Value: Exactly True Logic revisited.Andreas Kapsner & Umberto Rivieccio - 2023 - Journal of Philosophical Logic 52 (5):1417-1444.
    In this paper we re-assess the philosophical foundation of Exactly True Logic ($$\mathcal {ET\!L}$$ ET L ), a competing variant of First Degree Entailment ($$\mathcal {FDE}$$ FDE ). In order to do this, we first rebut an argument against it. As the argument appears in an interview with Nuel Belnap himself, one of the fathers of $$\mathcal {FDE}$$ FDE, we believe its provenance to be such that it needs to be taken seriously. We submit, however, that the argument ultimately fails, (...)
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  6.  17
    Fragments of Quasi-Nelson: The Algebraizable Core.Umberto Rivieccio - 2022 - Logic Journal of the IGPL 30 (5):807-839.
    This is the second of a series of papers that investigate fragments of quasi-Nelson logic (QNL) 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 |$FL_{ew}$| (full Lambek calculus with exchange and weakening) by the Nelson axiom. The algebraic counterpart of QNL (quasi-Nelson algebras) is a class of commutative integral residuated lattices (a.k.a. |$FL_{ew}$|-algebras) that includes both Heyting and Nelson algebras (...)
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  7. 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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  8. 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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  9.  82
    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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  10.  93
    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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  11.  76
    Representation of interlaced trilattices.Umberto Rivieccio - 2013 - Journal of Applied Logic 11 (2):174-189.
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  12. Priestley Duality for Bilattices.A. Jung & U. Rivieccio - 2012 - Studia Logica 100 (1-2):223-252.
    We develop a Priestley-style duality theory for different classes of algebras having a bilattice reduct. A similar investigation has already been realized by B. Mobasher, D. Pigozzi, G. Slutzki and G. Voutsadakis, but only from an abstract category-theoretic point of view. In the present work we are instead interested in a concrete study of the topological spaces that correspond to bilattices and some related algebras that are obtained through expansions of the algebraic language.
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  13. Dualities for modal N4-lattices.R. Jansana & U. Rivieccio - 2014 - Logic Journal of the IGPL 22 (4):608-637.
  14.  59
    Paraconsistent modal logics.Umberto Rivieccio - 2011 - Electronic Notes in Theoretical Computer Science 278:173-186.
    We introduce a modal expansion of paraconsistent Nelson logic that is also as a generalization of the Belnapian modal logic recently introduced by Odintsov and Wansing. We prove algebraic completeness theorems for both logics, defining and axiomatizing the corresponding algebraic semantics. We provide a representation for these algebras in terms of twiststructures, generalizing a known result on the representation of the algebraic counterpart of paraconsistent Nelson logic.
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  15.  89
    Neutrosophic logics: prospects and problems.Umberto Rivieccio - 2008 - Fuzzy Sets and Systems 159 (14):1860-1868.
    Neutrosophy has been introduced some years ago by Florentin Smarandache as a new branch of philosophy dealing with “the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra”. A variety of new theories have been developed on the basic principles of neutrosophy: among them is neutrosophic logics, a family of many-valued systems that can be regarded as a generalization of fuzzy logics. In this paper we present a critical introduction to neutrosophic logics, focusing on (...)
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  16. 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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  17.  20
    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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  18.  93
    Modal twist-structures over residuated lattices.H. Ono & U. Rivieccio - 2014 - Logic Journal of the IGPL 22 (3):440-457.
  19.  8
    Finite Hilbert Systems for Weak Kleene Logics.Vitor Greati, Sérgio Marcelino & Umberto Rivieccio - forthcoming - Studia Logica:1-27.
    Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar–Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics.
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  20.  54
    Residuated bilattices.Umberto Rivieccio & Ramon Jansana - 2012 - Soft Computing 16 (3):493-504.
    We introduce a new product bilattice con- struction that generalizes the well-known one for interlaced bilattices and others that were developed more recently, allowing to obtain a bilattice with two residuated pairs as a certain kind of power of an arbitrary residuated lattice. We prove that the class of bilattices thus obtained is a variety, give a finite axiomatization for it and characterize the congruences of its members in terms of those of their lat- tice factors. Finally, we show how (...)
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  21.  47
    Varieties of interlaced bilattices.Umberto Rivieccio, Ramon Jansana & Felix Bou Moliner - 2011 - Algebra Universalis 66 (1-2):115-141.
    The paper contains some algebraic results on several varieties of algebras having an (interlaced) bilattice reduct. Some of these algebras have already been studied in the literature (for instance bilattices with conflation, introduced by M. Fit- ting), while others arose from the algebraic study of O. Arieli and A. Avron’s bilattice logics developed in the third author’s PhD dissertation. We extend the representation theorem for bounded interlaced bilattices (proved, among others, by A. Avron) to un- bounded bilattices and prove analogous (...)
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  22.  32
    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 log- ics and prove a completeness result for the first and last element of the chain stating that both logics are determined by a single finite (...)
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  23.  14
    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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  24.  6
    Nelson algebras, residuated lattices and rough sets: A survey.Jouni Järvinen, Sándor Radeleczki & Umberto Rivieccio - 2024 - Journal of Applied Non-Classical Logics 34 (2-3):368-428.
    Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is currently lacking, and the theory of Nelson algebras remains largely unknown to most logicians. This paper aims to fill this gap by focussing on the essential developments in the field over the past two decades. Additionally, we explore generalisations of Nelson algebras, such as N4-lattices which (...)
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  25.  77
    Logiche polivalenti per l'Intelligenza Artificiale: il sistema di Ginsberg.Umberto Rivieccio - 2005 - Epistemologia 28 (1):25-44.
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  26.  82
    Finite axiomatizability of logics of distributive lattices with negation.Sérgio Marcelino & Umberto Rivieccio - forthcoming - Logic Journal of the IGPL.
    This paper focuses on order-preserving logics defined from varieties of distributive lattices with negation, and in particular on the problem of whether these can be axiomatized by means Hilbert-style calculi that are finite. On the negative side, we provide a syntactic condition on the equational presentation of a variety that entails failure of finite axiomatizability for the corresponding logic. An application of this result is that the logic of all distributive lattices with negation is not finitely axiomatizable; we likewise establish (...)
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  27.  72
    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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  28.  4
    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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  29.  2
    Some More Theorems on Structural Entailment Relations and Non-deterministic Semantics.Carlos Caleiro, Sérgio Marcelino & Umberto Rivieccio - 2024 - In Jacek Malinowski & Rafał Palczewski (eds.), Janusz Czelakowski on Logical Consequence. Springer Verlag. pp. 345-375.
    We extend classical work by Janusz Czelakowski on the closure properties of the class of matrix models of entailment relations—nowadays more commonly called multiple-conclusion logics—to the setting of non-deterministic matrices (Nmatrices), characterizing the Nmatrix models of an arbitrary logic through a generalization of the standard class operators to the non-deterministic setting. We highlight the main differences that appear in this more general setting, in particular: the possibility to obtain Nmatrix quotients using any compatible equivalence relation (not necessarily a congruence); the (...)
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  30.  13
    Multivalued logics for artificial intelligence: Ginsberg's system.Umberto Rivieccio - 2005 - Epistemologia 28 (1).
  31. What is abstract algebraic logic?Umberto Rivieccio - 2009 - Epistemologia 32 (2):255.