Normalization and cut-elimination theorems for some logics of evidence and truth
Logic
2024-06-03 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2405.20932,
title = {Normalization and cut-elimination theorems for some logics of evidence and truth},
author = {Marcelo E. Coniglio and Martín Figallo and Abilio Rodrigues},
journal= {arXiv preprint arXiv:2405.20932},
year = {2024}
}