This report is a detailed empirical examination of Suppes' ideas about the syntax and semantics of natural language, and an attempt at supporting the proposal that model-theoretic semantics of the type first proposed by Tarski is a useful tool for understanding the semantics of natural language. Child speech was selected as the best place to find data on natural language because it presents a view of the real problems represented by natural language, and because it allows the study of the process of language development. The main body of data consists of a series of recordings between a 32-month-old girl, Erica, and several adults. The ERIC corpus is found to be syntactically simpler and semantically more straightforward than adult speech. It is divided into utterances; its vocabulary is compared to ADULT vocabulary; a word frequency count is made; and its words are classified gramatically. A discussion follows of the standard concepts and results of the theory of generative grammars. A grammar for ERICA is devised, with special attention to lexical ambiguity. Mathematical syntax and semantics are discussed, followed by a description of ERICA semantics, with special reference to grammatical and semantic ambiguity. Conclusions include: (1) a reasonable probabilistic grammar for ERICA can be constructed; (2) the grammar GE1 is the best model for lexical disambiguation; (3) the grammar functions reasonably well semantically; (4) the notion of probability can play a key role in the construction of a semantics; and (5) simple set-theoretical functions are often successful in describing the ERICA semantics. (Author/AM)