Review

This is an incredibly well written paper on a central problem in description logics. Description logics are a family of logics for modeling complex hierarchical structures. In a description logic it is possible to define a terminology, which is a set of concepts definitions. Concept definitions describe their members by specifying necessary and sufficient conditions for membership. In a sense, concepts can be thought of as a set of views. Descriptions of concepts are built from a set of constructors that differ from one description logic to another. In addition to defining a terminology, a description logic knowledge base also includes a set of ground facts, stating membership of objects in a concept, or a relationship between pairs of objects. Description logic systems provide reasoning services such as: subsumption between concepts and determining whether an object belongs to a concept.

This paper considers the problem of determining whether a description logic knowledge base is satisfiable. As the authors explain, all the other reasoning problems can be reduced to satisfiability. The specific description logic that is considered is ALCNR, which is a relatively expressive logic. The paper presents a tableau based algorithm for satisfiability.

This paper was so clearly written that it enabled me to immediately start doing research in the area of description logics. The algorithm has several subtleties that the authors explain very well. I highly recommend this paper as a starting point into the theory of description logics.

For an overview of the use of description logics in data management, I recommend a paper by Alex Borgida [2].