BALC: A Belief Extension of Description Logic ALC

Description logics (DLs) are the logical foundations of semantic Web. The most basic DL is the attributive concept description language with complements (ALC). Other existing DLs are extended from ALC. All these DLs have an explosive entailment problem facing inconsistent knowledge. However, inconsistency is a main feature of general knowledge. Inconsistent knowledge frequently emerges in the practice of ontology engineering. It is important to extend DLs with the ability to deal with inconsistent knowledge. Belief is often used in para-consistent logic. A belief extension of ALC, named BALC is proposed to reasoning with inconsistency. By appending belief annotations to ALC atomic concepts and roles, syntax and semantic of BALC are defined. Inconsistent knowledge can be represented in BALC without causing the explosive entailment problem. Decidability is a key feature of DLs. By designing a tableau-based decision procedure for concept satisfiability problem, decidability of BALC is proved.