The simple phrase structure rules listed earlier have no recursive elements. Each time we start to create an S, we only create a single S (sentence structure). We actually need to be able to include sentence structures within other sentence structures. In traditional grammar, these “sentence structures” were described as “clauses.” We know, for example, that Mary helped George is a sentence. We can put this sentence inside another sentence beginning Cathy knew that [Mary helped George]. And, being tediously recursive, we can put this sentence inside another sentence beginning John believed that [Cathy knew that [Mary helped George]].

In these sentences, two new proper nouns and two new verbs have been used. We have to expand our earlier set of lexical rules to include PN → {John, Cathy} and V → {believed, knew}. After verbs such as believe and know, as in these examples, the word that introduces a complement phrase.