We consider non-Horn Deductive Data Bases (DDB) represented in a First Order language without function symbols. In this context the DDB is an incomplete description of the world. A rst approach to reduce the incompleteness is to add to the DDB some kind of default rules, in order to automatically assume missing information. The second approach, which is adopted in this paper, is to provide to the user the conditions which guarantee the validity of the answer. These conditional answers are generated by standard reasoning, and not by default reasoning. Then the problem is the following : if T represents the DDB and q the query, and if there is no direct answer to q, we want to derive the more general conditions c such that : T ` q c. We present a strategy, GASP, designed for this purpose. It is de ned by meta rules, and these meta rules can be used for a least xpoint operator de nition. We show that the GASP strategy is always more e cient than another usual strategy called GALP. Since ...