A hybrid approach for modeling uncertainty in terminological logics

Abstract

This paper proposes a probabilistic extension of terminological logics. The extension maintains the original performance of drawing inferences on a hierarchy of terminological definitions. It enlarges the range of applicability to real world domains determined not only by definitional but also by uncertain knowledge. First, we introduce the propositionally complete terminological language ALC. On the basis of the language construct “probabilistic implication”, it is shown how statistical information on concept dependencies can be represented. To guarantee (terminological and probabilistic) consistency, several requirements have to be met. Moreover, these requirements allow to infer implicitly existent probabilistic relationships and their quantitative computation. Consequently, our model applies to domains where both term descriptions and non-categorical relations between term extensions have to be represented.

This work has been carried out in the WIP project which is supported by the German Ministry for Research and Technology BMFT under contract ITW 8901 8. I would like to thank Bernhard Nebel, Bernd Owsnicki-Klewe, and Hans-Jürgen Profitlich for helpful comments on earlier versions of this paper.