Abstract narrative After an initial burst of activity in the 1960s, when it was founded, the field of mathematical linguistics has been comparatively quiescent in the past decade or so. Nonetheless, a few researchers have kept active in the field, and have periodically produced results which have had a major impact on general concerns of linguistic theory, such as the demon- stration that the generative power of transformational grammars, without special constraints, is greater than supposed, and the proof of the basic learnability theorem. The Principal Investigator of this proposal is one of those researchers who have continued to explore the mathe- matical properties of grammatical systems. He is a leading authority on the theory of computational complexity as it applies to formal grammars and parsing systems. He has now formulated the outlines of a new approach to the formal des- cription of syntactic structures, which incorporates as key elements a novel notation which combines the expressions of first-order logic with the the expressions of conventional phrase-structure grammars, and a view of languages as families of finite approximations, in place of the conventional mathe- matical view of a language as an infinite set of finite strings. The aim of the project is to develop the investigator's approach into a formal system which can be used as a tool for linguistic description, and which can be studied for its mathematical properties in new and potentially revealing ways. The investigator is being assisted in this endeavor by a collaborator who is an accomplished descriptive and theoretical linguist. The project has the potential to make significant new contributions to linguistic theory and also to computational linguistics.
