ABSTRACT
The chapter presents the development of a model-theoretic semantics for English sentences, which uses neither quantifiers nor variables, but only constants denoting given sets and relations, and operations on sets and relations. It aims to survey these developments and then consider some extensions to procedural semantics. A quite different sort of application of variable-free semantics to prosodic variations of negation is given in P. Suppes. A Boolean grammar is semantically correct if and only if it has a semantically valid model theory of the syllogism. The chapter outlines the beginnings of a theory of congruence for set-theoretical semantics in Suppes, but a psychologically realistic theory of congruence that takes into account not only procedures but also intentions and emotional states of speakers and listeners is needed as part of any empirically satisfactory theory of communication. Most of the notation is standard in elementary set theory.
