Control in Montague Grammar

The problem of interpreting "'missing" noun phrases in predicate structures has been a central concern of transformational theory since its inception. Recently, a number of linguists, under various versions of the "'extended standard theory", have dealt with this problem of "'control" (see Brame (1976), Bresnan (1972; 1978), Chomsky (1957; 1965; 1973; 1976), Chomsky and Lasnik (1977), Faraci (1974), Jackendoff (1972), Solan (1978), Wilkins (1977), Williams (1977)). Many of these writers share the assumption that control is to be determined by rules operating on intermediate structures of a certain sort that contain various abstract elements such as traces, empty nodes, and complementizers. Not so well known are treatments within a different tradition which has taken its inspiration from Richard Montague (see especially papers 6, 7, 8 in Montague (1974)). Common to all these treatments is the requirement that the fragments contain both an explicit set of syntactic rules and an explicit model-theoretical interpretation. We may view the results as systems which build "bottom-to-top" a syntactic structure and a corresponding representation of "logical form" (a structure in an interpreted intensional logic). The sole abstract elements are an infinite set of indexed pro-forms which underlie pronouns. Partee (1975a,b; 1976b), Thomason (1976), and Dowty (forthcoming) are among those who have addressed the sorts of problems we will be concerned with here. I wish to extend the treatments of these writers to cover some of the knottier problems that have been discussed in the recent transformational iterature. The specific framework I will use draws upon both the transformational and the Montague traditions.1 Montague has often been criticized for his views of syntax. A subsidiary aim of this article is to explore an approach to English syntax that is in the spirit of Montague's practice, especially in PTQ. It seems to me that Montague syntax offers an interesting alternative to transformational syntax of all varieties. Among the assumptions I will make are these: A. A grammar defines sets of structural descriptions. Each is an ordered pair: (a)

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