Syntax of a Montague grammar

In the current paper, I present a Montague-style syntax for a fragment of English. In order to acquaint the Reader with the meaning of the mathematical symbols used by Richard Montague, I illustrate each of the grammar rules defined by this American logician and a student of Alfred Tarski, with my own examples as Montague only gave two examples of usage of his grammar rules. I discovered that composing some of them gives rise to ungrammatical phrases. Moreover, I discuss the changes which Montague introduced when adapting Ajdukiewicz’s system of categories, and the consequences of these changes. I also explain the importance of intensional context and provide my own examples.