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 ( $$\textit{LET}_{J}$$ ). 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. $$\textit{LET}_{J}$$ 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 $$\textit{LET}_{J}$$ , as well as some technical results that fit the intended interpretation.