Subsumption and Reenement in Model Inference

In his famous Model Inference System, Shapiro 10] uses so-called reenement operators to replace too general hypotheses by logically weaker ones. One of these reenement operators works in the search space of reduced rst order sentences. In this article we show that this operator is not complete for reduced sentences, as he claims. We investigate the relations between subsumption and reenement as well as the role of a complexity measure. We present an inverse reduction algorithm which is used in a new reenement operator. This operator is complete for reduced sentences. Finally, we will relate our new reenement operator with its dual, a generalization operator, and its possible application in model inference using inverse resolution.