Explanations for Negative Query Answers under Existential Rules
İsmail İlkan Ceylan‚ Thomas Lukasiewicz‚ Enrico Malizia‚ Cristian Molinaro and Andrius Vaicenavičius
Ontology-mediated query answering is an extensively studied paradigm, where the conceptual knowledge provided by an ontology is leveraged towards a more enhanced querying of data sources. A major advantage of ontological reasoning is its interpretability, which allows one to derive explanations for query answers. Indeed, explanations have a long history in knowledge representation, and have also been investigated for ontology languages based on description logics and existential rules. Existing works on existential rules, however, merely focus on understanding why a query is entailed, i.e., explaining positive query answers. In this paper, we continue this line of research and address another important problem, namely, explaining why a query is not entailed under existential rules, i.e., explaining negative query answers, inspired by earlier studies based on description logics. We consider various problems related to explaining non-entailments from the abduction literature, and also introduce new problems. For all considered problems, we give a thorough complexity analysis for a wide range of existential rule languages and complexity measures.