Mind, Body, World- Foundations of Cognitive Science, 2013a

phrase is AP , where AP represents an adjective phrase. Because the same
symbol occurs on each side of the equation, the context-free grammar is recursive.
One can apply this rule repeatedly to insert clauses of the same type into a phrase.
This is shown in Figure 3-7, which illustrates phrase markers for noun phrases that
might apply to my dog Rufus. The basic noun phrase is the dog. If this recursive rule
is applied once, it permits a more elaborate noun phrase to be created, as in the cute
dog. Recursive application of this rule permits the noun phrase to be elaborated
indefinitely, (e.g., the cute brown scruffy dog).
(A)
NP
(B)
NP
Det
N
Det
N
Art
N
Art
AP
N
the
dog
the
A
N
cute
dog
(C)
NP
Det
N
Art
AP
N
the
A
cute
AP
A
AP
N
N
brown
A
N
scruffy
dog
Figure 3-7. Phrase markers for three noun phrases: (A) the dog, (B) the cute dog,
and (C) the cute brown scruffy dog. Note the recursive nature of (C).
The recursive nature of a context-free grammar is revealed in a visual inspection of a
phrase marker like the one illustrated in Figure 3-7C. As one inspects the figure, one
sees the same pattern recurring again and again, as was the case with the Sierpinski
triangle. The recursive nature of a context-free grammar produces self-similarity
Elements of Classical Cognitive Science 67