2024/05/31 by Marcelo E. Coniglio, Coniglio, Marcelo E., Martín Figallo +3
Computer Science · #Logic, Reasoning, and Knowledge #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.2405.20932
In this paper, we investigate proof-theoretic aspects of the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson's logic N and the logic of first-degree entailment FDE, also known as Belnap-Dunn four-valued logic, with a classicality operator that recovers classical logic for formulas in its scope. We will present natural deduction and sequent systems for LETJ and LETF, together with proofs of normalization and cut-elimination theorems, respectively. As a corollary, we obtain decidability for both logics.