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Two grammars for Chinese number names

Published online by Cambridge University Press:  27 June 2016

Barron Brainerd
Barron Brainerd*
Affiliation:
University of Toronto
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Extract

The purpose of this note is to introduce a restricted class of transformational grammars, the deletion grammars, and to use them to discuss the names of natural numbers in Chinese. Hereafter these names are referred to as Chinese number names.

Transformations and transformational grammars were introduced into linguistics by N. Chomsky. By now a vast literature on transformations has grown up. However, many of the transformational grammars appearing in this literature lack precision and rigor. In particular, it is not always clear what corpus they generate because of the multiplicity, complexity, and inadequate definition of the transformations contained in these grammars.

Type
Research Article
Information
Canadian Journal of Linguistics/Revue canadienne de linguistique , Volume 12 , Issue 1 , Fall 1966 , pp. 33 - 51
Copyright
Copyright © Canadian Linguistic Association 1966

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References

1 Natural numbers are the numbers used to count objects. For example, in English they are zero, one, two, three,…, one thousand two hundred eighty-five….

2 They were introduced in his thesis Transformational Analysis (University of Pennsylvania, 1955) and elaborated on in later works. For an introduction to transformations and transformational grammars, see E. Bach, An Introduction to Transformational Grammar (Holt, Rinehart and Winston 1964).

3 Katwijk, A. van, “A grammar of Dutch number names,” Foundations of Language, 1 (1965), pp. 51–58 Google Scholar.

4 Peng, Fred C. C., “The numeric system of standard Chinese.” Presented at the LSA Meeting, July 1965 (Ann Arbor, Michigan)Google Scholar; also Appendix III to “Fulcrum Technique for Chinese-English Machine Translation,” (Bunker-Ramo Corporation Report, July 1965).

5 The following set theoretic notations are used freely:

a ∈ A means a is an element of set A,

A ∪ B is the set of all elements which belong to either A, or B, or both A and B, and A ∩ B is the set of all elements in both A and B.

{a ∈ A\P(a)} stands for the set of all a ∈ A for which the statement P(a) is true, {a1, a2,…,an} for some n ≥ 1 stands for the set containing exactly the elements a1, a2,…,an.

A ⊂ B means A is a subset of B, that is, every element of A is also an element of B.

6 A single-value function f is composed of three parts: (i) a set Dom f , the domain of f; (ii) a second set Rang f , the range of f; and (iii) a rule f: x → f(x) which assigns to each x in Dom f a unique element f(x) in Rang f . Thus, for example, consider the function f where Dom f = Rang f = R, the set of real numbers, and f: x. → x2 . Here f associates with every real number its square. Note that Rang f contains numbers which are not images of x under f, (that is, in this case, Rang f contains numbers which are not squares.) A multiple-valued function is defined in the same way as a single-valued function except that condition (iii) is relaxed to the extent that there may be more than one value f(x) for each x in Dom f . An example is

where Dom f = Rang f = R and f(x) is eithe .

7 A string α over V is said to be a SUBSTRING of a string β over V if α = α1 α2 …αn, and β = β0 α1 β1 α2…βn-1 αn βn where n > 1, a, αi ∈ F(V) for i = 1, 2,…, n and βi∈ Fo(V) for i = 0,1,…,n. Note that we do not rule out the possibility that some or all of the βi equal Λ.

8 Joseph Needham and Wang Ling, Science and Civilization in China, Volume 3 (Cambridge, 1959), pp. 86ff. Needham’s list is not the only possible one. The Tai-p’ing yü-lan (Chüan 750) gives a different list for the lower series beyond chao.

9 Ibid., p. 87, footnote b.

10 Mullie, J., The Structural Principles of the Chinese Language (Peiping, 1932)Google Scholar.

11 Ren, Chao Yuen, Mandarin Primer (Cambridge, Mass., 1948)Google Scholar.

12 Ibid., p. 202.

13 Liang, which is an alternate expression for two, will not be used until we come to consider optional transformations toward the end of Section 4. It is included in VT(C0) for use at that time.

14 Mullie, Structural Principles, states that 4005 can be rendered *ssu ch’ien ling ling wu, but native speakers reject this string as a possible Chinese number name. 400S is rendered ssu ch’ien ling wu.

15 The reader will no doubt note that O1 is not a deletion. The optional replacement of erh by Hang is one aspect of Chinese number names which cannot be handled entirely in the framework of deletion grammar without introducing an inordinate amount of complication into the structure of the grammar. Therefore this one replacement transformation will be allowed.

16 Here the convention is used that (a, c) = (ch’ien, pai) (for example) means the same as a = ch’ien and b = pai. Thus (4.11) provides a shorthand list of the possible values of c and a.