Purpose is crucial for privacy protection as it makes users confident that their personal data are processed as intended. Available proposals for the specification and enforcement of purpose-aware policies are unsatisfactory for their ambiguous semantics of purposes and/or lack of support to the run-time enforcement of policies. In this paper, we propose a declarative framework based on a first-order temporal logic that allows us to give a precise semantics to purpose-aware policies and to reuse algorithms for the design of a run-time monitor enforcing purpose-aware policies. We also show the complexity of the generation and use of the monitor which, to the best of our knowledge, is the first such a result in literature on purpose-aware policies.