•  3
    Nelson’s logic
    with Thiago Nascimento, Umberto Rivieccio, and Matthew Spinks
    Logic Journal of the IGPL. forthcoming.
    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 res…Read more
  •  24
    The standard notion of formal theory, in logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed to accept. In reviewing the main abstract approaches to the study of logical consequence, we point out why this notion of theory is unsatisfactory at multiple levels, and introduce a novel notion of theory that attacks the shortcomings of the received notion …Read more
  •  10
    Correction to: Sequent Systems for Negative Modalities
    with Ori Lahav and Yoni Zohar
    Logica Universalis 13 (1): 135-135. 2019.
    In the original publication, the corresponding author was indicated incorrectly. The correct corresponding author of the article should be Ori Lahav. The original article has been updated accordingly.
  •  9
    Wittgenstein & Paraconsistência
    Principia: An International Journal of Epistemology 14 (1): 135-173. 2010.
    In classical logic, a contradiction allows one to derive every other sentence of the underlying language; paraconsistent logics came relatively recently to subvert this explosive principle, by allowing for the subsistence of contradictory yet non-trivial theories. Therefore our surprise to find Wittgenstein, already at the 1930s, in comments and lectures delivered on the foundations of mathematics, as well as in other writings, counseling a certain tolerance on what concerns the presence of cont…Read more
  •  17
    Sequent Systems for Negative Modalities
    with Ori Lahav and Yoni Zohar
    Logica Universalis 11 (3): 345-382. 2017.
    Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate semantics and proof systems, whose philosophical interpretations and computational properties are found wanting. In this paper we investigate congruential non-classical negations that live inside very natural systems of normal modal logics over complete distr…Read more
  •  35
    Nearly every normal modal logic is paranormal
    Logique Et Analyse 48 (189-192): 279-300. 2005.
    An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its negation are satisfied. Paraconsistent logics are negation-inconsistent yet non-overcomplete; paracomplet…Read more
  •  32
    Wittgenstein & Paraconsistência
    Principia: An International Journal of Epistemology 14 (1): 135-73. 2010.
    In classical logic, a contradiction allows one to derive every other sentence of the underlying language; paraconsistent logics came relatively recently to subvert this explosive principle, by allowing for the subsistence of contradictory yet non-trivial theories. Therefore our surprise to find Wittgenstein, already at the 1930s, in comments and lectures delivered on the foundations of mathematics, as well as in other writings, counseling a certain tolerance on what concerns the presence of cont…Read more
  •  7
    Doi:10.5007/1808-1711.2010v14n1p135
    Principia: An International Journal of Epistemology 14 (1): 135-73. 2010.
    In classical logic, a contradiction allows one to derive every other sentence of the underlying language; paraconsistent logics came relatively recently to subvert this explosive principle, by allowing for the subsistence of contradictory yet non-trivial theories. Therefore our surprise to find Wittgenstein, already at the 1930s, in comments and lectures delivered on the foundations of mathematics, as well as in other writings, counseling a certain tolerance on what concerns the presence of cont…Read more
  •  18
    On negation: Pure local rules
    Journal of Applied Logic 3 (1): 185-219. 2005.
  •  46
    Limits for Paraconsistent Calculi
    Notre Dame Journal of Formal Logic 40 (3): 375-390. 1999.
    This paper discusses how to define logics as deductive limits of sequences of other logics. The case of da Costa's hierarchy of increasingly weaker paraconsistent calculi, known as $ \mathcal {C}$n, 1 $ \leq$ n $ \leq$ $ \omega$, is carefully studied. The calculus $ \mathcal {C}$$\scriptstyle \omega$, in particular, constitutes no more than a lower deductive bound to this hierarchy and differs considerably from its companions. A long standing problem in the literature (open for more than 35 year…Read more
  •  22
    Generalizing truth-functionality
    Bulletin of Symbolic Logic 12 (3): 511-511. 2006.
  •  57
    Possible-translations semantics for some weak classically-based paraconsistent logics
    Journal of Applied Non-Classical Logics 18 (1): 7-28. 2008.
    In many real-life applications of logic it is useful to interpret a particular sentence as true together with its negation. If we are talking about classical logic, this situation would force all other sentences to be equally interpreted as true. Paraconsistent logics are exactly those logics that escape this explosive effect of the presence of inconsistencies and allow for sensible reasoning still to take effect. To provide reasonably intuitive semantics for paraconsistent logics has traditiona…Read more
  •  31
    Negative modalities, consistency and determinedness
    with Adriano Dodó
    Electronic Notes in Theoretical Computer Science 300 21-45. 2014.
    We study a modal language for negative operators—an intuitionistic-like negation and its paraconsistent dual—added to (bounded) distributive lattices. For each non-classical negation an extra operator is hereby adjoined in order to allow for standard logical inferences to be opportunely restored. We present abstract characterizations and exhibit the main properties of each kind of negative modality, as well as of the associated connectives that express consistency and determinedness at the objec…Read more
  •  75
    Logics of essence and accident
    Bulletin of the Section of Logic 34 (1): 43-56. 2005.
    We say that things happen accidentally when they do indeed happen, but only by chance. In the opposite situation, an essential happening is inescapable, its inevitability being the sine qua non for its very occurrence. This paper will investigate modal logics on a language tailored to talk about essential and accidental statements. Completeness of some among the weakest and the strongest such systems is attained. The weak expressibility of the classical propositional language enriched with the n…Read more
  •  117
    What is a Non-truth-functional Logic?
    Studia Logica 92 (2): 215-240. 2009.
    What is the fundamental insight behind truth-functionality ? When is a logic interpretable by way of a truth-functional semantics? To address such questions in a satisfactory way, a formal definition of truth-functionality from the point of view of abstract logics is clearly called for. As a matter of fact, such a definition has been available at least since the 70s, though to this day it still remains not very widely well-known. A clear distinction can be drawn between logics characterizable th…Read more
  •  176
    Formal inconsistency and evolutionary databases
    with Walter A. Carnielli and Sandra De Amo
    Logic and Logical Philosophy 8 (2): 115-152. 2000.
    This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems a…Read more