An ALC Description Default Logic with Exceptions-First

Knowledge formalization and reasoning automation are central within Artificial Intelligence. Classical logic has been traditionally used for such purposes. However, it is better suited to deal with complete knowledge in ideal circumstances. In real situations, in which the knowledge is partial, classical logic is not sufficient since it is monotonic. No monotonic logics have been proposed to better cope with practical reasoning. A successful formalization of no monotonic reasoning is Reiter's default logic which extends classical logic with default rules. Unfortunately, default logic is undividable. One reason for that is the use of classical logic as its monotonic basis. In this work, we change the default logic monotonic basis and propose a new default logic based on the description logic ALC. This new default logic is decidable and useful to formalize practical reasoning on hierarchical ontology's with exceptions, specially the ones that deals with legal knowledge and reasoning. On the default counterpart, we add some restrictions to the application of defaults in order to obtain nice properties such as coherence and elimination of anomalous extensions. We present the main algorithms used to build the extensions for this logic with its complexity analysis.