Learning Useful Horn Approximations

While the task of answering queries from an arbitrary propositional theory is intractable in general, it can typically be performed eeciently if the theory is Horn. This suggests that it may be more eecient to answer queries using a \Horn approximation"; i.e., a horn theory that is semantically similar to the original theory. The utility of any such approximation depends on how often it produces answers to the queries that the system actually encounters; we therefore seek an approximation whose expected \coverage" is maximal. Unfortunately, there are several obstacles to achieving this goal in practice: (i) The optimal approximation depends on the query distribution, which is typically not known a priori; (ii) identifying the optimal approximation is intractable, even given the query distribution; and (iii) the optimal approximation might be too large to guarantee tractable inference. This paper presents an approach that overcomes (or side-steps) each of these obstacles. We deene a learning process, AdComp, that uses observed queries to estimate the query distribution \online", and then uses these estimates to hill-climb, eeciently, in the space of size-bounded Horn approximations , until reaching one that is, with provably high probability, eeectively at a local optimum.