Uncertainty Reasoning for Ontologies with General TBoxes in Description Logic

We present a reasoning procedure for ontologies with uncertainty described in Description Logic (DL) which include General TBoxes, i.e., include cycles and General Concept Inclusions (GCIs). For this, we consider the description language ALCU , in which uncertainty parameters are associated with ABoxes and TBoxes, and which allows General TBoxes. Using this language as a basis, we then present a tableau algorithm which encodes the semantics of the input knowledge base as a set of assertions and linear and/or nonlinear arithmetic constraints on certainty variables. By tuning the uncertainty parameters in the knowledge base, different notions of uncertainty can be modeled and reasoned with, within the same framework. Our reasoning procedure is deterministic, and hence avoids possible empirical intractability in standard DL with General TBoxes. We further illustrate the need for blocking when reasoning with General TBoxes in the context of ALCU .