  On the Semantic Web, metadata and ontologies are used to enable computers to
read data. The Web Ontology Language (OWL) has been proposed as a standard
ontological language, and various inference systems for this language have been
studied. Description logics are regarded as the theoretical foundations of OWL;
they provide the syntax and semantics of a formal language for describing
ontologies and knowledge bases. In addition, tableau algorithms for description
logics have been developed as the standard reasoning algorithms for decidable
problems. However, tableau algorithms generate inefficient reasoning steps
owing to their nondeterministic branching for disjunction as well as the
increase in the size of models occasioned by existential quantification. In
this study, we propose conjunctive normal form (CNF) concepts, which utilize a
flat concept form for description logic ALC in order to develop algorithms for
reasoning about sets of clauses. We present an efficient reasoning algorithm
for clause sets where any ALC concept is transformed into an equivalent CNF
concept. Theoretically, we prove the soundness, completeness, and termination
of the reasoning algorithms for the satisfiability of CNF concepts.
