Open AccessNotes on the Logic of Perfect Paradefinite Algebras
Author(s) -
Joel Felipe Ferreira Gomes,
Vitor Greati
Publication year - 2021
Language(s) - English
Resource type - Conference proceedings
DOI - 10.5753/wbl.2021.15777
Subject(s) - interior algebra , variety (cybernetics) , algebraic logic , algebra over a field , mathematics , nest algebra , equivalence (formal languages) , intermediate logic , algebraic semantics , algebraic number , pure mathematics , computer science , jordan algebra , theoretical computer science , description logic , algebra representation , non associative algebra , mathematical analysis , statistics
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≤.