Counting Query Answers over a DL-Lite Knowledge Base (extended version)
This work addresses computational complexity for ontology-mediated query answering, which is incremental as it refines prior bounds in a specific domain.
The paper tackles the problem of counting query answers over DL-Lite knowledge bases, improving upon existing results by providing PTIME and coNP lower bounds and upper bounds in PTIME and LOGSPACE.
Counting answers to a query is an operation supported by virtually all database management systems. In this paper we focus on counting answers over a Knowledge Base (KB), which may be viewed as a database enriched with background knowledge about the domain under consideration. In particular, we place our work in the context of Ontology-Mediated Query Answering/Ontology-based Data Access (OMQA/OBDA), where the language used for the ontology is a member of the DL-Lite family and the data is a (usually virtual) set of assertions. We study the data complexity of query answering, for different members of the DL-Lite family that include number restrictions, and for variants of conjunctive queries with counting that differ with respect to their shape (connected, branching, rooted). We improve upon existing results by providing a PTIME and coNP lower bounds, and upper bounds in PTIME and LOGSPACE. For the latter case, we define a novel query rewriting technique into first-order logic with counting.