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

The complex, clausal structure of a natural language is instead captured by a
more powerful device—a Turing machine—that can accommodate the regularities
of a context-free grammar (e.g., Chomsky, 1957, 1965). A context-free grammar can
be described as a set of rewrite rules that convert one symbol into one or more other
symbols. The application of these rewrite rules produces a hierarchically organized
symbolic structure called a phrase marker (Radford, 1981). A phrase marker is a set
of points or labelled nodes that are connected by branches. Nonterminal nodes represent
lexical categories; at the bottom of a phrase marker are the terminal nodes
that represent lexical categories (e.g., words). A phrase marker for the simple sentence
Dogs bark is illustrated in Figure 3-6.
S
NP
N
N
dogs
VP
V
V
bark
Figure 3-6. A phrase marker for the sentence Dogs bark.
The phrase marker for a sentence can be illustrated as an upside-down tree whose
structure is grown from the root node S (for sentence). The application of the
rewrite rule S NP VP produces the first layer of the Figure 3-6 phrase marker,
showing how the nodes NP (noun phrase) and VP (verb phrase) are grown from S.
Other rewrite rules that are invoked to create that particular phrase marker are NP
, N, N dogs, VP , V, and V bark. When any of these rewrite
rules are applied, the symbol to the left of the is rewritten as the symbol or symbols
to the right. In the phrase marker, this means the symbols on the right of the
are written as nodes below the original symbol, and are connected to the originating
node above, as is shown in Figure 3-6.
In a modern grammar called x-bar syntax (Jackendoff, 1977), nodes like NP and
VP in Figure 3-6 are symbols that represent phrasal categories, nodes like and
are symbols that represent lexical categories, and nodes like “and” are symbols that
represent categories that are intermediates between lexical categories and phrasal
categories. Such intermediate categories are required to capture some regularities
in the syntax of natural human languages.
In some instances, the same symbol can be found on both sides of the in a
rewrite rule. For instance, one valid rewrite rule for the intermediate node of a noun
66 Chapter 3