The Generalized Counting Method for Recursive Logic Queries

This paper treats the problem of implementing efficiently recursive Horn Clauses queries, including those with function symbols. In particular, the situation is studied where the initial bindings of the arguments in the recursive query goal can be used in the top-down (as in backward chaining) execution phase to improve the efficiency and, often, to guarantee the termination, of the forward chaining execution phase that implements the fixpoint computation for the recursive query. A general method is given for solving these queries; the method performs an analysis of the binding passing behavior of the query, and then reschedules the overall execution as two fixpoint computations derived as results of this analysis. The first such computation emulates the propagation of bindings in the top-down phase; the second generates the desired answer by proving the goals left unsolved during the previous step. Finally, sufficient conditions for safety are derived, to ensure that the fixpoint computations are completed in a finite number of steps.