Database and Artificial Intelligence applications are briefly discussed and it is argued that they need deduction methods that are not only refutation complete but also complete for finite satisfiability. A novel deduction method is introduced for such applications. Instead of relying on Skolemization, as most refutation methods do, the proposed method processes existential quantifiers in a special manner which makes it complete not only for refutation, but also for finite satisfiability. A main contribution of this paper is the proof of these results.