Ontology-based Data Access: A Study through Disjunctive Datalog, CSP, and MMSNP

TL;DR

This paper explores the expressive power and computational properties of ontology-mediated queries, linking them to disjunctive datalog, CSPs, and MMSNP, and deriving new results on rewritability and complexity.

Contribution

It characterizes the expressive power of ontology-mediated queries, connects them to CSPs and MMSNP, and derives new complexity and rewritability results.

Findings

Characterization of query expressive power via disjunctive datalog fragments.

Connections established between ontology-mediated queries, CSPs, and MMSNP.

New results on first-order rewritability, P/NP dichotomy, and query containment.

Abstract

Ontology-based data access is concerned with querying incomplete data sources in the presence of domain-specific knowledge provided by an ontology. A central notion in this setting is that of an ontology-mediated query, which is a database query coupled with an ontology. In this paper, we study several classes of ontology-mediated queries, where the database queries are given as some form of conjunctive query and the ontologies are formulated in description logics or other relevant fragments of first-order logic, such as the guarded fragment and the unary-negation fragment. The contributions of the paper are three-fold. First, we characterize the expressive power of ontology-mediated queries in terms of fragments of disjunctive datalog. Second, we establish intimate connections between ontology-mediated queries and constraint satisfaction problems (CSPs) and their logical generalization, MMSNP formulas. Third, we exploit these connections to obtain new results regarding (i) first-order rewritability and datalog-rewritability of ontology-mediated queries, (ii) P/NP dichotomies for ontology-mediated queries, and (iii) the query containment problem for ontology-mediated queries.