Degree-preserving companion of Nelson logic expanded with a consistency operator - Esteva, Francesc; Orellano, Aldo Figallo; Flaminio, Tommaso; Godo, Lluís (Anais do Workshop Brasileiro de Lógica (WBL); 2020: Anais do I Workshop Brasileiro de LógicaDO - 10.5753/wbl.2020.11457, 2020)
The main aim of this paper is defining a Logic of Formal Inconsistency over the degree-preserving companion of Nelson logic with a consistency operator. In this sense, we present a quasivariety of Nelson lattices enriched with a suitable consistency operator and axiomatise the corresponding logic. As main results we present necessary and sufficient conditions to prove a categorial equivalence for the category for Nelson lattices with a consistency operator.