Natural Language Syntax and Semantics
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Abstract:
The treatment of natural language syntax and semantics presented here is based on an approach known as categorial grammar. The basic idea is that the syntactic categories of English and other natural languages are analogous to types in programming languages and typed logics. For example, an adjective, like "yellow " modifies a noun phrase like "bird " to give a new noun phrase "yellow bird". This can be treated formally by giving the word "bird" the type N and the word "yellow " the type N! N. The phrase "yellow bird" is then a well typed application of the adjectival operator "yellow " to the argument "bird". The phrase "bird yellow " is not well typed under this scheme and is not a grammatical noun phrase of English. Treating syntactic categories as types and assigning types to the individual words works surprisingly well as a theory of grammaticality in English. Although the basic categorial concepts do not account for all grammatical phenomenon, they do provide an integrated approach to syntax and semantics and clearly demonstrate the intimate relationship between syntactic categories and semantic types. The categorial grammar formalism can be used to essentially derive the basic syntactic categories of natural language from simple semantic considerations. In this section we present a very simple version of categorial grammar. This simple treatment only scratches the surface of the rich theories of natural language syntax that have evolved over the past thirty years. Pointers to more complete treatments are given at the end.
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