A distance-based framework for inconsistency-tolerant reasoning and inconsistency measurement in DL-Lite

In this paper, we present a distance-based framework for DL-Lite based on the notion of features. Within this framework, we propose a distance-based paraconsistent semantics for DL-Lite where meaningful conclusions can be rationally drawn even from an inconsistent knowledge base and we develop a distance-based inconsistency measurement for DL-Lite to provide more informative metrics which can tell the differences between axioms causing inconsistency and among inconsistent knowledge. Furthermore, we investigate several important logical properties (e.g., consistency preservation, closure consistency, splitting property etc.) of the entailment relation based on the new semantics and show its advantages in non-monotonic reasoning for DL-Lite. Finally, we show that our two distance-based inconsistency measures are basic inconsistency measures where some good properties hold such as Free Axiom Independence and Dominance of inconsistency etc.