Contraction and revision over DL-Lite TBoxes

Abstract

Two essential tasks in managing Description Logic (DL) ontologies are eliminating problematic axioms and incorporating newly formed axioms. Such elimination and incorporation are formalised as the operations of contraction and revision in belief change. In this paper, we deal with contraction and revision for the DL-Lite family through a model-theoretic approach. Standard DL semantics yields infinite numbers of models for DL-Lite TBoxes, thus it is not practical to develop algorithms for contraction and revision that involve DL models. The key to our approach is the introduction of an alternative semantics called type semantics which is more succinct than DL semantics. More importantly, with a finite signature, type semantics always yields finite humber of models. We then define model-based contraction and revision for DL-Lite TBoxes under type semantics and provide representation theorems for them. Finally, the succinctness of type semantics allows us to develop tractable algorithms for both operations.