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Profile: Joao Marcos (Universidade Federal do Rio Grande do Norte)
  1. Adriano Dodó & João Marcos (2014). Negative Modalities, Consistency and Determinedness. Electronic Notes in Theoretical Computer Science 300:21-45.
    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 object-language level. Appropriate sequent-style proof systems and adequate kripke semantics are also (...)
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  2. João Marcos (2011). Wittgenstein & Paraconsistência. Principia 14 (1):135-73.
    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 contradictions in a mathematical system. ‘Contradiction. Why just this (...)
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  3. João Marcos (2009). What is a Non-Truth-Functional Logic? Studia Logica 92 (2):215 - 240.
    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 through: (...)
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  4. Joao Marcos (2008). Possible-Translations Semantics for Some Weak Classically-Based Paraconsistent Logics. Journal of Applied Non-Classical Logics 18 (1):7-28.
    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 traditionally proven to be a challenge. Possible-translations (...)
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  5. Joao Marcos (2006). Generalizing Truth-Functionality. Bulletin of Symbolic Logic 12 (3):511-511.
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  6. Carlos Caleiro, Walter Carnielli, Marcelo Coniglio & João Marcos (2005). Two's Company: The Humbug of Many Logical Values. In J. Y. Beziau (ed.), Logica Universalis. Birkhäuser Verlag.
    The Polish logician Roman Suszko has extensively pleaded in the 1970s for a restatement of the notion of many-valuedness. According to him, as he would often repeat, “there are but two logical values, true and false.” As a matter of fact, a result by W´ojcicki-Lindenbaum shows that any tarskian logic has a many-valued semantics, and results by Suszko-da Costa-Scott show that any many-valued semantics can be reduced to a two-valued one. So, why should one even consider using logics with more (...)
     
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  7. Joao Marcos (2005). Logics of Essence and Accident. Bulletin of the Section of Logic 34 (1):43-56.
    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 non-normal modal operators of essence (...)
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  8. Joao Marcos (2005). Nearly Every Normal Modal Logic is Paranormal. Logique Et Analyse 48 (189-192):279-300.
    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; paracomplete logics are negation-incomplete yet non-overcomplete. A paranormal logic (...)
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  9. Walter A. Carnielli, João Marcos & Sandra De Amo (2000). Formal Inconsistency and Evolutionary Databases. Logic and Logical Philosophy 8 (2):115-152.
    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 are examples of what we dub Logics of Formal Inconsistency (LFI) (...)
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  10. Walter A. Carnielli & João Marcos (1999). Limits for Paraconsistent Calculi. Notre Dame Journal of Formal Logic 40 (3):375-390.
    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 years) is (...)
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