On Expansion and Contraction of DL-Lite Knowledge Bases

Knowledge bases (KBs) are not static entities: new information constantly appears and some of the previous knowledge becomes obsolete. In order to reflect this evolution of knowledge, KBs should be expanded with the new knowledge and contracted from the obsolete one. This problem is well-studied for propositional but much less for first-order KBs. In this work we investigate knowledge expansion and contraction for KBs expressed in DL-Lite, a family of description logics (DLs) that underlie the tractable fragment OWL 2 QL of the Web Ontology Language OWL 2. We start with a novel knowledge evolution framework and natural postulates that evolution should respect, and compare our postulates to the well-established AGM postulates. We then review well-known model and formula-based approaches for expansion and contraction for propositional theories and show how they can be adapted to the case of DL-Lite. In particular, we show intrinsic limitations of model-based approaches: besides the fact that some of them do not respect the postulates we have established, they ignore the structural properties of KBs. This leads to undesired properties of evolution results: evolution of DL-Lite KBs cannot be captured in DL-Lite. Moreover, we show that well-known formula-based approaches are also not appropriate for DL-Lite expansion and contraction: they either have a high complexity of computation, or they produce logical theories that cannot be expressed in DL-Lite. Thus, we propose a novel formula-based approach that respects our principles and for which evolution is expressible in DL-Lite. For this approach we also propose polynomial time deterministic algorithms to compute evolution of DL-Lite KBs when evolution affects only factual data.