Analytic proofs for logics of evidence and truth

Abstract

This paper presents a sound, complete, and decidable analytic tableau system for the logic of evidence and truth \letf, introduced in Rodrigues, Bueno-Soler \& Carnielli (Synthese, DOI: 10.1007/s11229-020-02571-w, 2020). \letf\ is an extension of the logic of first-degree entailment (\fde), also known as Belnap-Dunn logic. \fde\ is a widely studied four-valued paraconsistent logic, with applications in computer science and in the algebra of processes. \letf\ extends \fde\ in a very natural way, by adding a classicality operator \cons, which recovers classical logic for propositions in its scope, and a non-classicality operator \incon, dual of \cons.