Explaining query answers in lightweight ontologies : the DL-Lite case

Abstract

In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for DLs, where research focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer (explanation of positive answer), it is important to explain also why a given tuple is missing (explanation of negative answer).<br />We first address the problem of explaining positive query answers by providing an algorithmic solution to the procedure already outlined in the literature. Additionally, we employ the new algorithm to solve the explanation problem for inconsistency in DL-Lite ontologies.<br />In solving the problem of explaining negative answers to (U)CQ over ontologies, we adopt abductive reasoning, that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning tasks, we consider existence and recognition of an explanation, and relevance and necessity of a certain assertion for an explanation. We characterize the computational complexity of these problems for subset minimal and cardinality minimal solutions.