Wednesday, May 28, 2014

Chomsky: "Three Models for the Description of Language" (1956)

This is my favorite Chomsky text, perhaps after Syntactic Structures. It contains a comparison of finite-state, phrase-structure, and context-sensitive languages; it also suggests that a transformational theory is the most illuminating generative story for English sentences.

A structural ambiguity; p. 118.

Garden Varieties

Among other things, the paper contains the following examples of formal languages (p. 115):
  • "Mirror-image" sentences: aa, bb, abba, baab, aabbaa, …
  • Echo sentences: aa, bb, abab, baba, aabaab, …
  • Counting sentences: ab, aabb, aaabbb, …
The counting language is also used to show that the set of phrase-structure languages is a proper subset of the set of context-sensitive languages (p. 119).

A Markov model hidden states (and thus arbitrary dependence lengths); p. 116.

Irrelevant to Grammar

The paper also contains the familiar jump from a rejection of Markov models to a rejection of statistical models at large:
Whatever the other interest of statistical approximation in this sense may be, it is clear that it can shed no light on the problems of grammar. There is no general relation between the frequency of a string (or its component parts) and its grammaticalness. We can see this most clearly by considering such strings as
(14) colorless green ideas sleep furiously
which is a grammatical sentence, even though it is fair to assume that no pair of its words may ever have occurred together in the past. (p. 116)
there is no significant correlation between order of approximation and grammaticalness. If we order the strings of a given length in terms of order of approximation to English, we shall find both grammatical and ungrammatical strings scattered throughout the list, from top to bottom. Hence the notion of statistical approximation appears to be irrelevant to grammar. (p. 116)
I suppose "order of approximation" here means "probability" rather literally the "order of the Markov model" (otherwise the this assertion doesn't make much sense).

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