Nonstandard Inferences in Description Logics: The Story So Far

Abstract

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.

An algorithm based on counterfactuals for concept learning in the Semantic Web

“…The approximated concept level representatives 16 are: 16 Here msc * stands for the approximation of the most specific concept operator, a well-known non standard inference in DLs [3]. Notice that, in the example above, we did not detail the generalization step as there is more than one possibility as it will be shown in the empirical evaluation.…”

“…In particular, we study the problem of building up a concept definition starting from positive and negative examples of the target concept itself. This is the line of past [9] and present [3,14] research aiming at finding methods for the bottom-up construction of knowledge bases. It could be argued that the standard practice of ontology engineering concepts and properties are devised before populating the knowledge base with instances.…”

Instance-based retrieval by analogy

“…Unfortunately, for many non-trivial DL languages, such as ALC, the exact MSC may not be always expressed with a finite acyclic description [1] interpreted with the descriptive semantics presented earlier, yet it may be approximated [3,2], which is satisfactory for inductive approaches.…”

From Unstructured 3D Point Clouds to Structured Knowledge - A Semantics Approach

“…Baader (Baader, 2006) sketches the architecture of any KR system based on DLs. It could be seen the central theme of such a system is a Knowledge Base (KB).…”