Ideally, the grammar of a language should tell us whkh sequences of words form sentences and which sequences don’t. It is doubtful whether any existing grammar achieves this end for one of the natural languages, such as English, Russian or Chinese. However, logicians have constructed certain artificial languages (e. g. the prepositional calculus) together with a set of rules which distinguish between sentences (or well-formed formulas, as logicians prefer to call them) and non-sentences. While it is premature to attempt a complete description of English, partial grammars have been constructed.
In this paper we shall consider a fragment of English containing the names John and Jane, the verbs must, work, call, have, be, the adverb today, the conjunctions but and while and a few other words of the same types. We also admit inflected forms such as works, worked, working, etc. We shall attempt to-decide which sequences of these word-forms are sentences and which are not. Our grammar, if successful, must tell us that “John must have been calling Jane today” is a sentence, and that “John has must call Jane” is not a sentence. However, we may as well admit that many sentences will escape our net, owing to the fact that certain constructions, e. g. the gerund, will not be considered here.