On formal aspects of the epistemic approach to paraconsistency

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 both BLE and LET J . The meanings of the connectives of BLE and LET J , from the point of view of preservation of evidence, is explained with the aid of an inferential semantics. A formalization of the notion of evidence for BLE as proposed by M. Fitting is also reviewed here. As a novel result, the paper shows that LET J is semantically characterized through the so-called Fidel structures. Some opportunities for further research are also discussed

On Barrio, Lo Guercio, and Szmuc on Logics of Evidence and Truth

The aim of this text is to reply to criticisms of the logics of evidence and truth and the epistemic approach to paraconsistency advanced by Barrio [2018], and Lo Guercio and Szmuc [2018]. We also clarify the notion of evidence that underlies the intended interpretation of these logics and is a central point of Barrio’s and Lo Guercio & Szmuc’s criticisms

On philosophical motivations for paraconsistency: an ontology-free interpretation of the logics of formal inconsistency

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 paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we argue that an intuitive reading of the bivalued semantics for the logic mbC, a logic of formal inconsistency based on classical logic, fits in well with the basic ideas of an intuitive interpretation of contradictions. On this interpretation, the acceptance of a pair of propositions A and ¬A does not mean that A is simultaneously true and false, but rather that there is conflicting evidence about the truth value of A

Generalized explosion principles

Paraconsistency is commonly defined and/or characterized as the failure of a principle of explosion. The various standard forms of explosion involve one or more logical operators or connectives, among which the negation operator is the most frequent and primary. In this article, we start by asking whether a negation operator is essential for describing explosion and paraconsistency. In other words, is it possible to describe a principle of explosion and hence a notion of paraconsistency that is independent of connectives? A negation-free paraconsistency resulting from the failure of a generalized principle of explosion is presented first. We also derive a notion of quasi-negation from this and investigate its properties. Next, more general principles of explosion are considered. These are also negation-free; moreover, these principles gradually move away from the idea that an explosion requires a statement and its opposite. Thus, these principles can capture the explosion observed in logics where a statement and its negation explode only in the presence of additional information, such as in the logics of formal inconsistency.Comment: 28 pages, 1 figure. The final version of the article has been submitted for publication in the Special Issue of Studia Logica on Paraconsistenc

Opening address: Paraconsistent logic

I am honoured with and touched by the invitation of delivering the opening address of this Congress. Firstly, to see paraconsistent logic flourishing and growing, as we can readily see by simply glacing over the programme of this conference, is among one of my greatest joys. Secondly, and equally important, because this congress takes place in the University of Toruń.I am honoured for having lectured here, a most congenial and stimulating place, and could not think of a better place for a conference dedicated to the memory of Stanisław Jaśkowski. In particular, I am delighted for having had a correspondence with him, and although I was deprived of the pleasure of meeting him personally, I was fortunate enough for having collaborated with some of his disciples, such as L. Dubikajtis and T. Kotas. All and all, Toruń in particular and Poland in general are for me a second home, for all the kindness and care everyone has shown to me over several years, since my very first visit to this country

Paraconsistency and Consistency Understood as the Absence of the Negation of any Implicative Theorem

As is stated in its title, in this paper consistency is understood as the absence of the negation of any implicative theorem. Then, a series of logics adequate to this concept of consistency is defined within the context of the ternary relational semantics with a set of designated points, negation being modelled with the Routley operator. Soundness and completeness theorems are provided for each one of these logics. In some cases, strong (i.e., in respect of deducibility) soundness and completeness theorems are also proven. All logics in this paper are included in Lewis’ S4. They are all paraconsistent, but none of them is relevant