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-Lite"F extended with DBoxes. DL-Lite"F is a description logic tailored for data intensive applications and the data complexity of query answering in DL-Lite"F with ABoxes is tractable (in AC^0). 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 [email protected]? convenience

Combining Global and Local Merges in Logic-based Entity Resolution

In the recently proposed Lace framework for collective entity resolution, logical rules and constraints are used to identify pairs of entity references (e.g. author or paper ids) that denote the same entity. This identification is global: all occurrences of those entity references (possibly across multiple database tuples) are deemed equal and can be merged. By contrast, a local form of merge is often more natural when identifying pairs of data values, e.g. some occurrences of 'J. Smith' may be equated with 'Joe Smith', while others should merge with 'Jane Smith'. This motivates us to extend Lace with local merges of values and explore the computational properties of the resulting formalism.Comment: Accepted at KR 202

Queries with negation and inequalities over lightweight ontologies

While the problem of answering positive existential queries, in particular, conjunctive queries (CQs) and unions of CQs, over description logic ontologies has been studied extensively, there have been few attempts to analyse queries with negated atoms. Our aim is to sharpen the complexity landscape of the problem of answering CQs with negation and inequalities in lightweight description logics of the DL-Lite and EL families. We begin by considering queries with safe negation and show that there is a surprisingly significant increase in the complexity from AC0 to undecidability (even if the ontology and query are fixed and only the data is regarded as input). We also investigate the problem of answering queries with inequalities and show that answering a single CQ with one inequality over DL-Lite with role inclusions is undecidable. In the light of our undecidability results, we explore syntactic restrictions to attain efficient query answering with negated atoms. In particular, we identify a novel class of local CQs with inequalities, for which query answering over DL-Lite is decidable