Finding Optimal Derivation Strategies in Redundant Knowledge Bases

A backward chaining process uses a collection of rules to reduce a given goal to a sequence of database retrievals. A \derivation strategy" is an ordering on these steps, specifying when to use each rule and when to perform each retrieval. Given the costs of reductions and retrievals, and the a priori likelihood that each particular retrieval will succeed, one can compute the expected cost of any strategy, for answering a speciic query from a given knowledge base. Smi89] presents an algorithm that nds the minimal cost strategy in time (essentially) linear in the number of rules, for any disjunctive, irredundant knowledge base. This paper proves that the addition of redundancies renders this task NP-hard. Many Explanation-Based Learning systems work by adding in redundancies; this shows the complexities inherent in their task.