We propose an extension of logic programming where the user can specify, together with the initial query, the information he is interested in by means of a request. This allows one to extract a result from an incomplete computation, such as the prefix of an infinite derivation. The classical property of independence of the selection rule doesn't hold anymore. It is shown that under mild conditions a class of selection rules can be identified for which independence holds. A model-theoretic semantics for the language is given.