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Since Chen's Entity-Relationship (ER) model, conceptual modelling has been playing a fundamental role in relational data design. In this paper we consider an extended ER model enriched with cardinality constraints, disjunction assertions, and is-a relations among both entities and relationships; we present a framework in which the data underlying an ER schema can be directly queried through the schema by using suitable predicates. In this setting, we consider the case of incomplete data, which is likely to happen, for instance, when data from different sources are integrated. We address the problem of providing correct answers to conjunctive queries by reasoning on the schema. Based on previous results about decidability of the problem, we provide a query answering algorithm based on rewriting the initial query into a recursive Datalog query, in which the information about the schema is encoded.We finally give some complexity results, and we show extensions to more general settings.