Abstract The tastes of a user can be represented in a natural way by using qualitative preferences. In this paper, we explore how ontological knowledge expressed via existential rules can be combined with CP-theories to (i) represent qualitative preferences along with domain knowledge, and (ii) perform preference-based answering of conjunctive queries (CQs). We call these combinations ontological CP-theories (OCP-theories). We define skyline and k-rank answers to CQs based on the user’s preferences encoded in an OCP-theory, and provide an algorithm for computing them. We also provide precise complexity (including data tractability) results for deciding consistency, dominance, and CQ skyline membership for OCP-theories.