Generalized Horn Constraints and Tractable Inference on Type Hierarchies with Open Specification

Large type hierarchies are an integral part of many databases, including in particular lexicons for natural-language parsers. Due to their size and complexity, it is often impractical to provide a complete specification. Rather, an open specification is employed, in which properties of the hierarchy are specified by constraints. Unfortunately, the great expressive power of open specification comes at the expense of considerable computational complexity, with essential tasks rendered NPhard. For this reason, most existing systems use a very simple set of default rules to determine the semantics, thus limiting the most desirable feature of open specification – wide expressive power. In this work, it is shown how open specification with a relatively expressive set of constraints may be realized, while still keeping the computational complexity within reasonable limits. The key to the approach is to replace the full logical formulas of general open specification with formulas based upon a special class of disjunctions of Horn sentences. The resulting time complexity, while greater than the linear complexity of propositional Horn inference, is still better than quadratic, and close to linear in many cases.