Default reasoning with inconsistent knowledge

A novel theory 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 prepositional formulas are defined such that the semantic link between a literal and its negation is split. Most theorems of default logic can be reproduced in the setting of the bi-default logic. It is proven that the bi-default logic is a generalization of the default logic in the presence of inconsistency. A method is provided as an alternative approach for making the reasoning ability of paraconsistent logic as powerful as the classical one.EI071030-10411