We discuss the use of model building for temporal representations. We chose Polish to illustrate our discussion because it has an interesting aspectual system, but the points we wish to make are not language specific. Rather, our goal is to develop theoretical and computational tools for temporal model building tasks in computational semantics. To this end, we present a first-order theory of time and events which is rich enough to capture interesting semantic distinctions, and an algorithm which takes minimal models for first-order theories and systematically attempts to ``perturb'' their temporal component to provide non-minimal, but semantically significant, models.