Review - Decidable Reasoning in Terminological Knowledge Representation Systems. 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.