We present here a continuation of our work presented in [Dem97]. We recall definitions of valid subsets or complete subsets of a database, and the modal logic that is used for reasoning about assumptions on validity and completeness, in order to characterise subsets of a standard answer that are either valid or complete. We formally define several forms of answers that are either extensional or intensional. Then, we analyse which kinds of anwers are really useful for users. Finally, we present an automated deduction method to compute these answers. This method is based on SOL-deduction, which has been designed for classical logic, and we show how it can be adapted to our modal logic.