An epistemic approach to paraconsistency: a logic of evidence and truth

Abstract

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 (BLE ), and extends it to the Logic of Evidence and Truth (LETJ ). The latter is a logic of formal inconsistency and undeterminedness that is able to express not only preservation of evidence but also preservation of truth. LETJ is anti-dialetheist in the sense that, according to the intuitive interpretation proposed here, its consequence relation is trivial in the presence of any true contradiction. Adequate semantics and a decision method are presented for both BLE and LETJ , as well as some technical results that fit the intended interpretation.

A Four-Valued Dynamic Epistemic Logic

“…The second negation (˜) is classical:˜ϕ means that it is not the case that ϕ. We can see the propositional fragment of FVEL (Definition 1.1) as a logic that preserves evidence, a concept mentioned in a recent paper by Carnielli and Rodrigues (2019).…”

“…The logic developed here can be compared to other epistemic logics in the literature that also deal with evidence (Renne 2009;van Benthem and Pacuit 2011;Baltag et al 2012Baltag et al , 2014Carnielli and Rodrigues 2019;Fitting 2017).…”

“…The closest works to ours have been developed roughly in parallel with it (see Santos 2018), and come in two very recent papers (Carnielli and Rodrigues 2019;Fitting 2017). First, Carnielli and Rodrigues (2019) develop the basic logic of evidence (BLE), which is a propositional logic similar to FDE and whose philosophical motivations are closely related to FVEL's. As mentioned in Sect.…”

Foreword: Consistency, Contradiction, and Consequence

“…The author defends the thesis that pure logics do not have canonical (standard) interpretations. As a special case, the author analyses the paraconsistent logics BLE and L E T j , proposed by Carnielli and Rodrigues in [2] and motivated by the idea of capturing contradictions as conflicting evidence and rejecting true contradictions (dialetheias). He shows that, despite such motivation, they are not incompatible with true contradictions.…”

A Brief Note on Béziau’s “Rather Trivial Theorem” About LP

“…These observations seem trivial to me, but I think it is necessary to state them again given the recent wave of attempts to warm up the war between the paraconsistent traditions, with talk about of the dialetheists' lies about the Liar [Arenhart and Melo, 2018], the antidialetheist evidence-based paraconsistent logic [Carnielli and Rodrigues, 2017], the incoherence of dialetheism [Arenhart and Melo, 2017], and so on. 1 Dialetheism has several contentious elements, for sure, but the alleged triviality of LP is not to be counted among them.…”