On the Universal Generation Problem for Unification Grammars

The universal generation problem for unification grammars is the problem of determining whether a given grammar derives any terminal string with a given feature structure. It is known that the problem is decidable for LFG and PATR grammars if only acyclic feature structures are taken into consideration. In this brief note, we show that the problem is undecidable for cyclic structures. This holds even for grammars that are off-line parsable.

Towards Modular Development of Typed Unification Grammars

Development of large-scale grammars for natural languages is a complicated endeavor: Grammars are developed collaboratively by teams of linguists, computational linguists, and computer scientists, in a process very similar to the development of large-scale software. Grammars are written in grammatical formalisms that resemble very-high-level programming languages, and are thus very similar to computer programs. Yet grammar engineering is still in its infancy: Few grammar development environments support sophisticated modularized grammar development, in the form of distribution of the grammar development effort, combination of sub-grammars, separate compilation and automatic linkage, information encapsulation, and so forth. This work provides preliminary foundations for modular construction of (typed) unification grammars for natural languages. Much of the information in such formalisms is encoded by the type signature, and we subsequently address the problem through the distribution of the signature among the different modules. We define signature modules and provide operators of module combination. Modules may specify only partial information about the components of the signature and may communicate through parameters, similarly to function calls in programming languages. Our definitions are inspired by methods and techniques of programming language theory and software engineering and are motivated by the actual needs of grammar developers, obtained through a careful examination of existing grammars. We show that our definitions meet these needs by conforming to a detailed set of desiderata. We demonstrate the utility of our definitions by providing a modular design of the HPSG grammar of Pollard and Sag.