Toward the Formal Verification of a Unification System $^{\ast }$

Unification grammars are widely used for encoding human knowledge. For unification systems, one major difficulty is the debugging of rules. In this paper, the authors suggest a novel method based on model checking to theoretically verify a complex grammar system for a unification-based parser. We propose the modeling method of the grammar and, more importantly, the abstraction method to compress the state space. We apply partial Kripke structures to model the rules. We prove that the state space can be reduced by several orders of magnitude while still keeping the behaviors of a non-compressed one. Practical verification issues are discussed, including the restrictions on specifications, the properties to check, etc. The proposed method will contribute to the effective debugging and application of unification grammars.