Understanding Inexpressibility of Model-Based ABox Evolution in DL-Lite (Extended Version)

Evolution of Knowledge Bases (KBs) expressed in Description Logics (DLs) has gained a lot of attention recently. Recent studies of the topic mostly focused on model-based approaches (MBAs), where the evolution of a KB results in a set of models. For KBs expressed in tractable DLs, such as those of the DL-Lite family, which we consider here, it was shown that one is faced with inexpressibility of evolution, i.e., the result of evolution of a DL-Lite KB in general cannot be expressed in DL-Lite. What is still missing in these studies is a thorough understanding of various important aspects of the evolution problem for DL-Lite KBs: in which fragments can evolution be captured? What causes the inexpressibility? Which logic is sufficient to express evolution? Can one approximate evolution in DL-Lite, and if yes, how? This work provides some understanding of these issues for an important class of quite natural MBAs, which cover the case of both update and revision. We describe what causes inexpressibility, and we propose techniques (based on what we call prototypes) that help to approximate evolution according to the well-known Winslett’s approach, which is inexpressible in DL-Lite. We also identify DL-Lite fragments for which evolution is expressible, and for such fragments we provide polynomial-time algorithms to compute the result of evolution.