Non-standard Inferences in Description Logics: The Story So Far

Description logics (DLs) are a successful family of logic-based knowledge representation formalisms that can be used to represent the terminological knowledge of an application domain in a structured and formally well-founded way. DL systems provide their users with inference procedures that allow to reason about the represented knowledge. Standard inference problems (such as the subsumption and the instance problem) are now well-understood. Their computational properties (such as decidability and complexity) have been investigated in detail, and modern DL systems are equipped with highly optimized implementations of these inference procedures, which—in spite of their high worst-case complexity—perform quite well in practice. In applications of DL systems it has turned out that building and maintaining large DL knowledge bases can be further facilitated by procedures for other, nonstandard inference problem, such as computing the least common subsumer and the most specific concept, and rewriting and matching of concepts. While the research concerning these non-standard inferences is not as mature as the one for the standard inferences, it has now reached a point where it makes sense to motivate these inferences within a uniform application framework, give an overview of the results obtained so far, describe the remaining open problems, and give perspectives for future research in this direction.