Horn Approximations of Empirical Data

Formal AI systems traditionally represent knowledge using logical formulas. Sometimes, however, a model-based representation is more compact and enables faster reasoning than the corresponding formula-based representation. The central idea behind our work is to represent a large set of models by a subset of characteristic models. More speci cally, we examine model-based representations of Horn theories, and show that there are large Horn theories that can be exactly represented by an exponentially smaller set of characteristic models. We show that deduction based on a set of characteristic models requires only polynomial time, as it does using Horn theories. More surprisingly, abduction can be performed in polynomial time using a set of characteristic models, whereas abduction using Horn theories is NP-complete. Finally, we discuss algorithms for generating e cient representations of the Horn theory that best approximates a general set of models.