11 found
Order:
See also
Abilio Rodrigues
Federal University of Minas Gerais
  1.  58
    An Epistemic Approach to Paraconsistency: A Logic of Evidence and Truth.Walter Carnielli & Abilio Rodrigues - 2019 - Synthese 196 (9):3789-3813.
    The purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which true contradictions are not tolerated. Contradictions are, instead, epistemically understood as conflicting evidence, where evidence for a proposition A is understood as reasons for believing that A is true. The paper defines a paraconsistent and paracomplete natural deduction system, called the Basic Logic of Evidence, and extends it to the Logic of Evidence and Truth. The latter is a logic of (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   18 citations  
  2. Towards a Philosophical Understanding of the Logics of Formal Inconsistency.Walter Carnielli & Abílio Rodrigues - 2015 - Manuscrito 38 (2):155-184.
    In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically justify (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  3.  8
    Measuring Evidence: A Probabilistic Approach to an Extension of Belnap–Dunn Logic.Abilio Rodrigues, Juliana Bueno-Soler & Walter Carnielli - forthcoming - Synthese:1-30.
    This paper introduces the logic of evidence and truth \ as an extension of the Belnap–Dunn four-valued logic \. \ is a slightly modified version of the logic \, presented in Carnielli and Rodrigues. While \ is equipped only with a classicality operator \, \ is equipped with a non-classicality operator \ as well, dual to \. Both \ and \ are logics of formal inconsistency and undeterminedness in which the operator \ recovers classical logic for propositions in its scope. (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  4.  8
    On Epistemic and Ontological Interpretations of Intuitionistic and Paraconsistent Paradigms.Walter Carnielli & Abilio Rodrigues - forthcoming - Logic Journal of the IGPL.
    From the technical point of view, philosophically neutral, the duality between a paraconsistent and a paracomplete logic lies in the fact that explosion does not hold in the former and excluded middle does not hold in the latter. From the point of view of the motivations for rejecting explosion and excluded middle, this duality can be interpreted either ontologically or epistemically. An ontological interpretation of intuitionistic logic is Brouwer’s idealism; of paraconsistency is dialetheism. The epistemic interpretation of intuitionistic logic is (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  5. On Formal Aspects of the Epistemic Approach to Paraconsistency.Walter Carnielli, Marcelo E. Coniglio & Abilio Rodrigues - 2018 - In Max Freund, Max Fernandez de Castro & Marco Ruffino (eds.), Logic and Philosophy of Logic: Recent Trends in Latin America and Spain. London: College Publications. pp. 48-74.
    This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LET J ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson’s logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability are given for (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  6.  4
    Recovery Operators, Paraconsistency and Duality.Walter Carnielli, Marcelo E. Coniglio & Abilio Rodrigues - 2020 - Logic Journal of the IGPL 28 (5):624-656.
    There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express metalogical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the logics of formal inconsistency and by the logics of formal undeterminedness. LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the validity of (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  7.  15
    Kripke-Style Models for Logics of Evidence and Truth.Henrique Antunes, Walter Carnielli, Andreas Kapsner & Abilio Rodrigues - 2020 - Axioms 9 (3).
    In this paper, we propose Kripke-style models for the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson’s logic N4 and the logic of first-degree entailment with a classicality operator ∘ that recovers classical logic for formulas in its scope. According to the intended interpretation here proposed, these models represent a database that receives information as time passes, and such information can be positive, negative, non-reliable, or reliable, while a formula ∘A means that the information about (...)
    No categories
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  8.  5
    Inferential Semantics, Paraconsistency, and Preservation of Evidence.Walter Carnielli & Abilio Rodrigues - 2019 - In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency. Springer Verlag. pp. 165-187.
    Proof-theoretic semantics provides meanings to the connectives of intuitionistic logic without the need for a semantics in the standard sense of an attribution of semantic values to formulas. Meanings are given by the inference rules that, in this case, do not express preservation of truth but rather preservation of availability of a constructive proof. Elsewhere we presented two paraconsistent systems of natural deduction: the Basic Logic of Evidence and the Logic of Evidence and Truth. The rules of BLE have been (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  9. On Philosophical Motivations for Paraconsistency: An Ontology-Free Interpretation of the Logics of Formal Inconsistency.Walter Carnielli & Abilio Rodrigues - manuscript
    In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non- contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  10.  6
    Foreword: Consistency, Contradiction, and Consequence.Abílio Rodrigues & Federico Matías Pailos - 2018 - Principia: An International Journal of Epistemology 22 (1):01-05.
    Foreword : Consistency, Contradiction, and Consequence.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  11.  8
    Paraconsistent Logic: Consistency, Contradiction and Negation.Abilio Rodrigues - forthcoming - History and Philosophy of Logic:1-7.
    The book Paraconsistent Logic: Consistency, Contradiction and Negation by Walter Carnielli and Marcelo Coniglio is the most thorough study of Logics of Formal Inconsistency...
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark