The second of Chomsky’s ‘three models for the description of language’, is Phrase Structure Grammar. Any set of sentences that can be generated by a finite state grammar can be generated by a phrase structure grammar. But the converse does not hold: there are sets of sentences that can be generated by a phrase structure grammar, but not by a finite state grammar. To express the relationship between phrase structure grammars and finite state grammars, we might say that phrase structure grammars are intrinsically more powerful than finite state grammars (they can do everything that finite-state grammars can do- and more).

Consider the following English sentence: The man hit the ball. It is made up of five words out of which the sentence is composed as its ultimate constituents. The order in which the ultimate constituents occur relative to one another may be described as the linear structure of the sentence. A traditionally minded grammarian might say, of our simple model sentence, that it has a subject and a predicate; that the subject is a noun phrase(NP), which consists of the definite article(T) and a noun(N); and that the predicate is a verb phrase(VP), which consists of a verb(V) with its object, which, like the subject, is a noun phrase consisting of the definite article and a noun. Essentially the same kind of description would have been given by ‘Bloomfieldian’ linguists in terms of the notions of immediate constituent analysis: the ‘immediate constituents’ of the sentence (the two phrases into which it can be analysed at the first stage) are the noun phrase the man (which has the role, or function of the subject), and the verb phrase hit the ball (which has the function of the predicate); that the immediate constituents of the man are the article the and the noun man; that the immediate constituents of hit the ball are the verb hit and the noun phrase the ball (which has the function of the object); and that the immediate constituents of the ball are the article the and the noun ball.

The notion of constituent structure or phrase structure (to use Chomsky’s term), is comparable with the notion of bracketing, in mathematics or symbolic logic. If we have an expression of the form x(y + z), we know that the operation of addition must be carried out first and the operation of multiplication afterwards. By contrast, x x y + z is interpreted (by means of the general convention that, in the absence of brackets, multiplication takes precedence over addition) as being equivalent to (x x y) + z. Generally speaking, the order in which the operations are carried out will make a difference to the result. For instance, with x = 2, y = 3 and z = 5 : x x (y + z) = 16, whereas (x x y)+ z = 11. There are many sequences of words in English and other languages that are ambiguous in much the same way that x x y + z would be ambiguous if it were not for the prior adoption by mathematicians of the general convention that multiplication takes precedence over addition.

A classic example is the phrase old men and women (and more generally A N and N) which may be interpreted either as (old men) and women – (xy) + z or old (men and women) – x(y + z). With the phrase structure indicated, by means of brackets, as old (men and women) the string of words is semantically equivalent to (old men) and (old women) — x(y + z) = (xy) + (xz). The theoretical importance of this phenomenon lies in the fact that the ambiguity of such strings as old men and women cannot be accounted for by appealing to a difference in the meaning of any of the ultimate constituents or to a difference of linear structure. Chomsky’s formalization of phrase structure grammar may be illustrated by means of the following rules:

(1) Sentence- NP + VP
(2) NP- T + N
(3) VP – Verb + NP
(4) T – the
(5) N – {man, ball…}
(6) Verb – {hit, took…}

This set of rules which will generate only a small fraction of the sentences of English is a simple phrase structure grammar. Each of these rules is of form X -> Y, where X is a single element and Y is a string consisting of one or more elements. The terminal string generated by the rules is the + man+ hit + the + ball, and it takes nine steps to generate this string of words. The set of nine strings, including the initial string, the terminal string and seven intermediary strings constitute a derivation of the sentence The man hit the ball in terms of this particular phrase structure grammar.

Operation of Rewriting

Whenever we apply a rule we put brackets, as it were, around the string of elements that are introduced by the rule and we label the string within the brackets as an instance of the element that has been rewritten by the rule. An alternative and equivalent means of representing the labelled bracketing assigned to strings of elements generated by a phrase structure grammar is a tree diagram. Since tree diagrams are visually clearer than sequences of symbols and brackets, they are more commonly used in the literature. The labelled bracketing, associated with a terminal string generated by a phrase structure is called a phrase marker.

The revolutionary step that Chomsky took, as far as linguistics is concerned, was to draw upon this branch of mathematics and apply it to natural languages, like English, rather than to the artificial languages constructed by logicians and computer scientists. But he did more than simply take over and adapt for the use of linguists an existing system of formalization and a set of theorems proved by others. He made an independent and original contribution to the study of formal systems from a purely mathematical point of view. The mathematical investigation of phrase structure grammar is now well advanced, and various degrees of equivalence has been proved which also formalise the notion of bracketing or immediate constituent structure.

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Devika Panikar has been teaching English Language and Literature for 14 years now. She is an Assistant Professor with the Directorate of Collegiate Education under the Government of Kerala. She teaches at the Government Colleges coming under this directorate and is now posted at the Department of English, H.H. The Maharaja’s Government College for Women, Thiruvananthapuram. This website is a collection of the lecture notes that she prepared by referring various sources, for her students’ perusal. It has been compiled here for the sake of future generations.

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