A Coherent and Paraconsistent Variant of the Default Logic

Reiter’s default logic is supposed to reasoning on consistent knowledge; when inconsistencies or contradictions are present in a default theory, no useful conclusions can be extracted. In the past years, fragments and variants of the default logic are proposed to avoid or handle inconsistencies or contradictions. Unfortunately, the expressive and reasoning power of these fragments are strictly weaker than the full version of Reiter’s default logic, and the semantics of the variants are changed even when the default theory is consistent and contradiction-free. In this paper, we propose a paraconsistent Annotated Default Logic, in which, the existence of non-trivial annotated extensions is guaranteed. In addition, the same conclusions are extracted as Reiter’s default logic does, as long as the default theory has non-trivial extensions in Reiter’s default logic. As a consequent, the intended meaning of the default theories are kept unchanged when shifting to our method. As a by product, the extra information presented in the annotated extensions can help the users in analyzing and modifying their knowledge representations.