On the convergence of query evaluation

We propose a "sideways information passing" method for evaluating Horn clause queries in the presence of monotonicity constraints on the database relations. We give a necessary and sufficient condition for its convergence and show that testing for the condition is polynomial when the arity of the relations is bounded, and PSPACE-complete otherwise. We also prove a related condition for the case of downward finite domains (e.g., Herbrand universes), thus improving an algorithm by Naish for a class of Prolog programs.