A Paraconsistent Route to Semantic Closure

BARRIO, EDUARDO ALEJANDRO; PAILOS, FEDERICO MATÍAS; SZMUC, DAMIÁN

LOGIC JOURNAL OF THE IGPL (PRINT)

OXFORD UNIV PRESS

Lugar: Oxford; Año: 2017

1367-0751

We will present a three-valued paraconsistent theory of truth calledMSCTT, which validates the naive T-Scheme, has the means to recaptures classical logic and is functionally complete. We reach these goals by adopting aweak self-referential procedure, that makes essential use of a peculiar biconditional. A comparison is presented with two theories that use a strong selfreferential procedure: LPconTT (Graham Priest?s system LP with a consistencyoperator and a transparent truth predicate) and MPTTT (a theory of truthbased on Coniglio and Silvestrini?s three-valued logic of formal inconsistency).It is later shown that those theories lead to triviality, while a non-trivialityproof is presented for MSCTT. Finally, we present a disjunctive sequent system called LSCTT, and prove that LSCTT is sound and complete with respectto our system.