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, while 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.
Highlights
IntroductionThe aim of this paper is to present Kripke-style models for the logics of evidence and truth LETJ and LETF , introduced in [1,2]
[2] Section 2.2.1.) Conclusive evidence is subjected to classical logic, and non-conclusive to a paraconsistent and paracomplete logic that is N4 in the case of LETJ and first-degree entailment (FDE) in the case of LETF
Sound and complete valuation semantics were presented for LETJ and LETF in [1,2], respectively
Summary
The aim of this paper is to present Kripke-style models for the logics of evidence and truth LETJ and LETF , introduced in [1,2]. The semantic values True, False, Both and None, of what became known as Belnap–Dunn 4-valued logic, express the circumstances in which the computer receives, respectively, only positive, only negative, conflicting and no information at all, about a proposition A. In addition to these four scenarios, LETJ and LETF are capable of representing two additional scenarios: when ○A does not hold, we have the four scenarios above, but when ○A holds, exactly one among A and ¬A holds, which means that the information about A, positive or negative, is reliable and subjected to classical logic.
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