Paraconsistent default reasoning

In this paper, a novel technique called bi-default theory is proposed for handling inconsistent knowledge simultaneously in the context of default logic without leading to triviality of the extension. To this end, the positive and negative transformations of propositional formulas are defined such that the semantic link between a literal and its negation is split. It is proven that the bi-default theory preserves many nice properties of Reiter’s original theory and guarantees the existence of consistent modified bi-extensions. Thus, the bi-default logic is a generalization of default logic in the presence of inconsistency. Furthermore, a method is provided as an alternative approach for making the reasoning ability of paraconsistent logic as powerful as classical one.