Nonmonotonic Description Logics – Requirements, Theory, and Implementations

Abstract

The Semantic Web and a number of modern knowledge-based applications have turned ontologies into a familiar and popular ICT notion. Description Logics (DLs) are one of the major formalisms for encoding ontologies.

Many “users” of such formalisms – that is, ontologies writers – would appreciate DLs to have nonmonotonic features. For example, it would be appealing to describe taxonomies by means of general default properties that may be later overridden in special cases; a similar behavior is supported by all object-oriented languages, after all. However, nonmonotonic extensions of DLs involve many tricky technical problems.

This talk will briefly illustrate some of the major requirements for nonmonotonic description logics and some of the formalisms currently available. Then we shall point out the major problems that still have to be solved in order to apply standard tableaux optimization techniques to nonmonotonic DLs. Since DLs are usually at least PSPACE-hard, such optimization techniques are crucial in making these formalisms usable in practice.

For example, it seems very difficult to find a tableaux system for a fragment of nonmonotonic DLs where a tableau needs not be stored entirely in memory (because it is enough to construct and verify a single branch at each iteration, for example).

Since “traditional” nonmonotonic semantics are not completely satisfactory, it may be possible to solve both semantic shortcomings and optimization problems by adopting suitable new logics.