Constraint propagation in kimmo systems

Abstract

Taken abstractly, the two-level (Kimmo) morphological framework allows computationally difficult problems to arise. For example, N + 1 small automata are sufficient to encode the Boolean satisfiability problem (SAT) for formulas in N variables. However, the suspicion arises that natural-language problems may have a special structure - not shared with SAT - that is not directly captured in the two-level model. In particular, the natural problems may generally have a modular and local nature that distinguishes them from more "global" SAT problems. By exploiting this structure, it may be possible to solve the natural problems by methods that do not involve combinatorial search. We have explored this possibility in a preliminary way by applying constraint propagation methods to Kimmo generation and recognition. Constraint propagation can succeed when the solution falls into place step-by-step through a chain of limited and local inferences, but it is insufficiently powerful to solve unnaturally hard SAT problems. Limited tests indicate that the constraint-propagation algorithm for Kimmo generation works for English, Turkish, and Warlpiri. When applied to a Kimmo system that encodes SAT problems, the algorithm succeeds on "easy" SAT problems but fails (as desired) on "hard" problems.