This paper introduces a generalization of weak model-theoretic forcing of [Rob71] and [Kei73]. This generalized forcing preserves classic properties of weak model-theoretic forcing, e.g. Generic Set Theorem (Thm. 3.23), Generic Model Theorem (Thm. 3.24, Thm. 4.8), and Henrard's Theorem (Thm. 5.8). It is applied in this paper to investigate a deductive model for updating a deductive data base with incomplete information, whose possible variations are restricted to certain finite sets of atomic or negated atomic first-order sentences. Moreover, the paper introduces the notion of pragmatic truth pertinent to those models, and characterizes it in terms of generalized forcing (Thm. 5.11).