Kripke-Style Models for Logics of Evidence and Truth

Abstract

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 (FDE) 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, and a formula ∘A means that the information about A, either positive or negative, is reliable. This proposal is in line with the interpretation of N4 and FDE as information-based logics, but adds to the four scenarios expressed by them two new scenarios: reliable (or conclusive) information (i) for the truth and (ii) for the falsity of a given proposition.

Non-contingency in a paraconsistent setting

“…3 . F as described in[7, Definitions 2 and 7]. Furthermore, •φ is interpreted as 'the information on φ is reliable' which is also similar to how we interpret (cf.…”

Paraconsistency, Evidence and Semantic Incompleteness

“…(oA∧oB)→o(A∧B) (3) (oA∧oB)→o(A⋁B) (4) Indeed, as Antunes et al (2020) emphasize, we do not obtain the consequent o(A∧B) in (3) because the semantic clause of o does not give us sufficient semantic information about A and B, and a similar reason applies to (4). However, in what follows, we argue that both formulas should be valid according to the evidence interpretation of LET J .…”

“…Such valuations are taken as tools for proving metatheoretical results such as soundness and completeness. Antunes et al (2020) provide a Kripke semantics for BLE, where the logical connectives of this logic are interpreted in a more intuitive way. But, as we said before, the natural deduction rules of Definition 2.1 are taken to give meaning to the connectives of BLE.…”

Evidências e dependência ontológica: sobre interpretações de lógicas paraconsistentes

“…Nesse caso, os cenários i-iv são interpretados como informação não confiável e correspondem aos quatro valores da lógica FDE que vimos na seção 2.3, e os cenários v e vi são interpretados como informação confiável, e esta é considerada sujeita à lógica clássica (cfe. Antunes et al 2020).…”