In ontology-based data access (OBDA), databases are connected to an ontology via mappings from queries over the database to queries over the ontology. In this paper, we define an ASP-based semantics for mappings from relational databases to first-order ontologies, augmented with queries over the ontology in the mapping rule bodies. The resulting formalism can be described as ”ASP modulo theories”, and can be used to express constraints and exceptions in OBDA systems, as well as being a powerful mechanism for succinctly representing OBDA mappings. Furthermore, we show that brave reasoning in this setting has either the same data complexity as ASP, or is at least as hard as the complexity of checking entailment for the ontology queries. Moreover, despite the interaction of ASP rules and the ontology, most properties of ASP are preserved. Finally, we show that for ontologies with UCQ-rewritable queries there exists a natural reduction from our framework to ASP with existential variables
