A formal framework for description logics with uncertainty

Description logics (DLs) play an important role in the Semantic Web as the foundation of ontology language OWL DL. On the other hand, uncertainty is a form of deficiency or imperfection commonly found in real-world information/data. In this paper, we present a framework for knowledge bases with uncertainty expressed in the description logic ALCU, which is a propositionally complete representation language providing conjunction, disjunction, existential and universal quantifications, and full negation. The proposed framework is equipped with a constraint-based reasoning procedure that derives a collection of assertions as well as a set of linear/nonlinear constraints that encode the semantics of the uncertainty knowledge base. The interesting feature of our approach is that, by simply tuning the combination functions that generate the constraints, different notions of uncertainty can be modeled and reasoned with, using a single reasoning procedure. We establish soundness, completeness, and termination of the reasoning procedure. Detailed explanations and examples are included to describe the proposed completion rules.