Since Chen's Entity-Relationship (ER) model, conceptual modeling has been playing a fundamental role in relational data design. In this paper we consider an extended ER (EER) model enriched with cardinality constraints, disjointness assertions, and is-a relations among both entities and relationships. In this setting, we consider the case of incomplete data, which is likely to occur, for instance, when data from different sources are integrated. In such a context, 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 that performs rewriting of the initial query into a recursive Datalog query encoding the information about the schema. We finally show extensions to more general settings. This paper will appear in the special issue of Theory and Practice of Logic Programming (TPLP) titled Logic Programming in Databases: From Datalog to Semantic-Web Rules.