Query Answering with DBoxes is Hard

Data in description logic knowledge bases is stored in the form of an ABox. ABoxes are often confusing for developers coming from relational databases because an ABox, in contrast to a database instance, provides an incomplete specification. A recently introduced assertional component of a description logic knowledge base is a DBox, which behaves more like a database instance. In this paper, we study the data complexity of query answering in the description logic DL-LiteF extended with DBoxes. DL-LiteF is a description logic tailored for data intensive applications and the data complexity of query answering in DL-LiteF with ABoxes is tractable (in AC0). Our main result is that this problem becomes coNP-complete with DBoxes. In some expressive description logics, query answering with DBoxes also leads to a higher (combined) complexity than query answering with ABoxes. As a proof of concept, we relate query answering in ALCFIO, i.e., ALC with Functional and Inverse roles, and nOminals to the same problem in ALCFI with DBoxes. The exact complexity of the former is an open problem in the description logic literature. Here we show that query answering in ALCFIO and ALCFI with DBoxes are mutually reducible to each other in polynomial time.All the proofs in this paper are available in the appendix for the reviewersʼ convenience.