Notes on the Logic of Perfect Paradefinite Algebras


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.

Palavras-chave: perfect paradefinite algebras, involutive Stone algebras, perfection operator, paradefinite logics, LFIUs


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GOMES, Joel Felipe Ferreira; GREATI, Vitor Rodrigues. Notes on the Logic of Perfect Paradefinite Algebras. In: WORKSHOP BRASILEIRO DE LÓGICA (WBL), 2. , 2021, Evento Online. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2021 . p. 41-48. ISSN 2763-8731. DOI: