Complexity Results for Paraconsistent Inference Relations

In this paper, the complexity of several paraconsistent inference relations, based on multivalued logics, is investigated. Many inference relations pointed out so far by Arieli and Avron, Besnard and Schaub, D’Ottaviano and da Costa, Frisch, Levesque, Priest are considered from the computational side. All these relations can be gathered into two categories: the basic ones stem directly from the notions of models within 3 or 4-valued logics, while the refined ones are based on notions of preferred models for such logics. Completing complexity results by Cadoli and Schaerf (centered on the basic relations), we show that the refined paraconsistent inference relations that have been defined in the framework of multivalued logics are highly intractable. Especially, we prove that the inference problems corresponding to these relations are Πp2complete, even in the simple case where the database is a CNF formula and the query is a propositional symbol.