Minimal Logical Constraint Covering Sets

We propose a general framework for computing minimal set covers under class of certain logical constraints. The underlying idea is to transform the problem into a mathematical programm under linear constraints. In this sense it can be seen as a natural extension of the vector quantization algorithm proposed by [5]. We show which class of logical constraints can be cast and relaxed into linear constraints and give an algorithm for the transformation. We provide two examples and two applications show the practical relevance of our approach.