Entailment Functions and Reasoning Under Inconsistency

This study proposes an intuitive and flexible framework for defining a large variety of paraconsistent entailment relations. We first introduce a notion named entailment function (EF) that is used for associating a value called entailment degree to every pair of belief base and formula. Then, we introduce our EF-based framework for defining paraconsistent entailment relations. Finally, we discuss a connection between the notion of entailment function and that of inconsistency measure.