On the Problem of Weighted Max-DL-SAT and its Application to Image Labeling

For a number of problems, such as ontology learning or image labeling, we need to handle uncertainty and inconsistencies in an appropriate way. Fuzzy and Probabilistic Description Logics are the two major approaches for performing reasoning with uncertainty in Description Logics, but modeling problems such as image labeling still remains difficult and handling inconsistencies is only supported to a limited extent. In this paper, we propose Max-DL-SAT and Weighted Max-DL-SAT as new reasoning services for Description Logics knowledge bases, which applies the idea behind Weighted Max-SAT to Description Logics and leads to a more intuitive representation of certain problems. It supports handling of uncertainty and inconsistencies. The contribution of this paper is threefold: We define a novel reasoning service on Description Logics knowledge bases, introduce an algorithm for solving such problems, and show the application of it to the problem of image labeling.