Edwin Samuel Williams

The unifying theme of this collection of papers by the very creative Russian mathematician I. M. Gelfand and his co-workers is the representation theory of groups and lattices. Two of the papers were inspired by application to theoretical physics; the others are pure mathematics though all the papers will interest mathematicians at quite opposite ends of the subject. Dr. G. Segal and Professor C-M. Ringel have written introductions to the papers which explain the background, put them in perspective and make them accessible to those with no specialist knowledge in the area.

This important monograph summarizes, rethinks, and extends a decade of the author's work on the role assignments--the ways in which the roles implied by verbs of a given type play out in terms of position and other syntactic functions. The study of theta roles and the locality of theta-role assignment leads into many interesting areas of linguistic theory, such as scope, the ECP, X-bar theory, binding theory, and the weak crossover condition; Williams's reconstruction thus offers a systematic integration of a remarkably wide range of syntactic phenomena. Williams starts by outlining a theory of the clause, specifically, of the distribution of Nominative Case and Tense. He then develops a formalism for the notion of "external argument" that is used throughout the rest of the book. Subsequent chapters review the issues surrounding the syntactic expression of the subject-predicate relationship, extend the notion of external argument to include NP movement, and reanalyze the verb movement constructions as deriving from the calculus of theta roles rather than movement. The last chapter distinguishes referential dependence and coreference, showing that a general Leftness condition governs the former, while the binding theory restated in terms of theta relations governs the latter.