This is a joint award with Dr. Joshi at the University of Pennsylvania. This team has proposed several major research tasks in natural language processing with special emphasis on several mathematical and computational aspects. The work clearly has a formal and mathematical character. The various computational structures and strategies the team has developed and will develop, need to be investigated mathematically becausesuch investigations shed light on the descriptive and processing powers of these formalisms. These two aspects, i.e., the development of the structures and strategies, and their mathematical investigations, are very much interrelated. It is believed that natural language processing backed up by a formal framework, and mathematical investigations grounded in empirical studies are two very productive areas of research. The researcher will focus on interested in mathematical investigations only to the extent to which the results have important implications for natural language processing.