Abstract We study the problem of associating formal semantic descriptions to data services. We base our proposal on the Ontology-based Data Access paradigm, where a domain ontology is used to provide a semantic layer mapped to the data sources of an organization. The basic idea is to explain the semantics of a data service in terms of a query over the ontology. We illustrate a formal framework for this problem, based on the notion of source-toontology (s-to-o) rewriting, which comes in three variants, called sound, complete and perfect, respectively. We present a thorough complexity analysis of two computational problems, namely verifification (checking whether a query is an s-to-o rewriting of a given data service), and computation (computing an s-to-o rewriting of a data service)