Inconsistencies, Negations and Changes in

The ability to deal with inconsistency and to accommodate change is of utmost importance in real-world applications of Description Logic based ontological reasoning and management [1]. For example, one of the typical scenarios in deployed Semantic Web applications is ontology reuse, where users build their own ontologies from existing ones, rather than starting from scratch. After adding new axioms into an existing ontology, users may find that revised ontologies become inconsistent. A remedy for such a situation would require the removal of a minimal part of the ontology in order to make the resulting ontology consistent [2]. This type of change is usually required to meet some rationality postulates, similar to those in the AGM theory in the belief revision. Addressing effectively the issues raised requires precise, formal definitions of inconsistency and negation. Unfortunately, DL-based ontology languages, such as OWL DL, do not provide enough expressive power to represent axiom negations. Furthermore, there is no single, well-accepted notion of inconsistency and negation in the Semantic Web community, due to the lack of a common and solid foundational framework. [4] proposed an approach to debug inconsistent ontologies, in which inconsistency is identified with the existence of unsatisfiable concepts. [3] developed a framework of reasoning with inconsistent ontologies, in which inconsistency is given a classical first-order logic interpretation. In [2], the definition of axio