Explanations for Negative Query Answers under Inconsistency-Tolerant Semantics

Inconsistency-tolerant semantics have been proposed to provide meaningful query answers even in the presence of inconsistent knowledge. Recently, explainability has also become a prominent problem in different areas of AI. While the complexity of inconsistency-tolerant semantics is rather well-understood, not much attention has been paid yet to the problem of explaining query answers when inconsistencies may exist. Recent work on existential rules in the inconsistent setting has focused only on understanding why a query is entailed. In this paper, we address another important problem, which is explaining why a query is not entailed under an inconsistency-tolerant semantics. In particular, we consider three popular semantics, namely, the ABox repair, the intersection of repairs, and the intersection of closed repairs. We provide a thorough complexity analysis for a wide range of existential rule languages and for several complexity measures.