🤖 AI Summary
This paper addresses inconsistent-tolerant query answering over prioritized knowledge bases—comprising logical theories, factual databases, and priority relations among conflicting facts. We systematically support query evaluation under three classical semantics—AR (cautious), IAR (intersection of all repairs), and brave—over two classes of optimal repair models: Pareto-optimal and completion-based repairs. Our key contribution is the first unified SAT encoding framework capable of handling arbitrary priority relations, enabling joint modeling and efficient solving for both repair classes and all three semantics. Based on this encoding, we implement ORBITS, a novel reasoning system. Experimental results demonstrate that ORBITS significantly outperforms baseline approaches across all semantics, highlighting the critical impact of semantic choice and solving strategy on performance. The work establishes a new paradigm for practical reasoning over inconsistent prioritized knowledge bases.
📝 Abstract
We investigate practical algorithms for inconsistency-tolerant query answering over prioritized knowledge bases, which consist of a logical theory, a set of facts, and a priority relation between conflicting facts. We consider three well-known semantics (AR, IAR and brave) based upon two notions of optimal repairs (Pareto and completion). Deciding whether a query answer holds under these semantics is (co)NP-complete in data complexity for a large class of logical theories, and SAT-based procedures have been devised for repair-based semantics when there is no priority relation, or the relation has a special structure. The present paper introduces the first SAT encodings for Pareto- and completion-optimal repairs w.r.t. general priority relations and proposes several ways of employing existing and new encodings to compute answers under (optimal) repair-based semantics, by exploiting different reasoning modes of SAT solvers. The comprehensive experimental evaluation of our implementation compares both (i) the impact of adopting semantics based on different kinds of repairs, and (ii) the relative performances of alternative procedures for the same semantics.
