Degree-preserving companion of Nelson logic expanded with a consistency operator

• Francesc Esteva Consejo Superior de Investigaciones Científicas http://orcid.org/0000-0003-4466-3298
• Aldo Figallo Orellano UNICAMP http://orcid.org/0000-0001-5844-3371
• Tommaso Flaminio Consejo Superior de Investigaciones Científicas http://orcid.org/0000-0002-9180-7808
• Lluís Godo Consejo Superior de Investigaciones Científicas http://orcid.org/0000-0001-6568-654X

DOI: https://doi.org/10.5753/wbl.2020.11457

Resumo

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.

Palavras-chave: Nelson lattices, Consistency operators, Logics of formal inconsistency

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