Nominalization and Montague Grammar: A semantics without types for natural languages

Abstract

We started from the fact that type theory, in the way it was implemented in IL, makes it costly to deal with nominalization processes. We have also argued that the type hierarchy as such doesn't play any real role in a grammar; the classification it provides for different semantic objects is already contained, in some sense, in the categorial structure of the grammar itself. So, on the basis of a theory of properties (Cocchiarella's HST*) we have tried to build a language (IL*) whose syntax does not contain any explicit typing of expressions. Some of the consequences that this move brings about in the overall organization of the grammar can be summarized as follows: (a) it allows for a simple treatment of infinitives, gerunds, factives and, in general, all those phenomena which might be analyzed as cases of nominalization; (b) it provides a simpler and more constrained semantics than IL, since IL* doesn't go beyond second order, and its non-modal basis is axiomatizable; (c) it suggests that the role of logical form in a theory of grammar could be that of a family of theories of semantic objects; (d) it eliminates the extrinsic limitations of a type hierarchy on the choice of the system of syntactic categories.