A MILP-based decision procedure for the (Fuzzy) Description Logic ALCB

ABSTRACT. Description Logics (DLs) have succeeded as a knowledge representation formalism in many domains of application. Nevertheless, they are not suitable to represent vague or imprecise information. To overcome this limitation, several fuzzy extensions have been proposed in the literature. An important family of reasoning algorithms for fuzzy DLs are based on a combination of tableaux algorithms and optimization problems. However, existing algorithms so far cannot support nominals.

In this paper, we give a step in this direction by studying the more specific case of value restrictions. In particular, we propose a novel reasoning algorithm for a fuzzy DL with value restrictions and functional roles. Interestingly, the tableaux algorithm is deterministic and does not need any guessing when dealing with nominal nodes.