Notes on the Logic of Perfect Paradefinite Algebras - Gomes, Joel Felipe Ferreira; Greati, Vitor Rodrigues (Anais do Workshop Brasileiro de Lógica (WBL), 2021)
This work introduces the variety of perfect paradefinite algebras (PPalgebras), consisting of De Morgan algebras enriched with a perfect operator o, which turns out to be equivalent to the variety of involutive Stone algebras (IS-algebras). The corresponding order-preserving logic PP ≤ is a Logic of Formal Inconsistency, a Logic of Formal Undeterminedness, a C -system and a D -system, some of these features being evident in the proposed axiomatization of PP-algebras. After proving the mentioned algebraic equivalence, we show how to axiomatize, by means of Hilbert-style calculi, certain extensions of De Morgan algebras with a perfect operator and, in particular, the logic PP ≤ .