Department of Computer, Control and Management Engineering

Query answering for Knowledge Bases (KBs) amounts to extracting information from the various models of a KB, and presenting the user with an object that represents such information. In the vast majority of cases, this object consists of those tuples of constants that satisfy the query expression either in every model (certain answers) or in some model (possible answers). However, similarly to the case of incomplete databases, both these forms of answers are a lossy representation of all the knowledge inferable from the query and the queried KB. In this paper, we illustrate a formal framework to characterize the information that query answers for KBs are able to represent. As a frst application of the framework, we study the informativeness of current query answering approaches, including the recently introduced partial answers. We then defne a novel notion of answers, allowing repetition of variables across answer tuples. We show that these answers are capable of representing a meaningful form of information, and we also study their data complexity properties.