Ahans at 13:28, 27 June 2006

2006-06-27T13:28:35Z

Ahans at 15:14, 17 June 2006

2006-06-17T15:14:25Z

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'''1. Problem and history'''

Depth (of embedding) of a syntactic construction is defined as the „number of steps from S to the given constituent, by applying production rules“ (Köhler, Altmann 2000). In practice, the sentence is analyzed in form of a graph-theoretical tree and the depth is the length of the way from S to the given symbol. The problem is to find the distribution of depth (x) in a text or in a corpus.

The first concept of depth was proposed by Yngve (1960, 1961). Different reserchers used it for typological purposes (Householder 1960; Papp 1966; Altmann, Lehfeldt 1973). It can be defined in the framework of any grammat. Köhler (1999) studied the dependence of depth on position (see Vol. 2); Köhler and Altmann (2000) derived the distribution of depth in a corpus.

'''2. Hypothesis'''

''The depth of syntactic construction abides by the hyper-Pascal distribution.''

'''3. Derivation'''

For the derivation the following quantities are necessary (Köhler, Altmann 2000)
minT – the requirement of limiting the depth of embedding which represents the limitation of the language processing memory;
maxH – the requirement of maximazing compactness. This enables us diminishing the complexity of the subordinated level of embedding by embedding constituents into the given level… minX on the level m corresponds to the requirement maxH on the level m+1;
E – a variable representing the average degree of fullness, the default value of complexity.

Assumptions: Depth x is directly proportional to depth x-1, the proportionality being given by the default value of complexity E. The requirement maxH increases the tendency towards greater depth, minT restricts is.
Thus we obtain

(1)<math> P_x= \frac{maxH + x}{minT + x}EP_{x-1}</math>.

Setting maxH = k-1, minT = m-1, E = q and solving (1) results in the hyperpascal distribution

(2)<math> P_x= \frac{{k+x-1 \choose x}}{{m+x-1 \choose x}}q^x P^0, x=0,1,2,...</math>

where <math> P_0^{-1} = _2 F_1 (k,1;m;q)</math> .

'''Example''': The distribution of depth in the Susanne corpus

Köhler and Altmann (2000) considered the depth of embedding in the Susanne corpus and obtained the results presented in Table 1 and Fig. 1.

Table 1
Fitting the hyper-Pascal distribution to the depth of the Susanne corpus

<div align="center">[[Image:Grafik1_DoSC.jpg]]</div>
<div align="center">Fig. 1. Fitting the hyper-Pascal distribution to the data in Table 1</div>

Since the sample size is very great (N = 101138), the usual chi-square test is inappropriate. Instead, one used the contingency coefficient <math>C = X^2/N</math>, which yields satisfactory results.

'''4. Authors:''' G. Altmann

'''5. References'''

'''Altmann, G., Lehfeldt,W.''' (1973). ''Allgemeine Sprachtypologie''. München: Fink.

'''Householder, F.W.Jr'''. (1960). First thoughts on syntactic indices. ''International Journal of American Linguistics 26, 195-197''.

'''Köhler, R'''. (1999). Syntactic structures: Properties and interrelations. ''J. of Quantitative Linguistics 6, 46-57''.

'''Köhler, R., Altmann, G.''' (2000). Probability distributions of syntactic units and properties. ''J. of Quantitative Linguistics 7, 189-200''.

'''Papp, F.''' (1966). On the depth of Hungarian sentences. ''Linguistics 25, 58-77''.

'''Yngve, V.''' (1960). A model and a hypothesis for language structure. ''Proceedings of the American Philosophical Society 104, 444-446''.

'''Yngve, V'''. (1961). The depth hypothesis. In: Jakobson, R. (ed.), ''Structure of Language and ist Mathematical Aspects: 130-138.'' Providence, R:I.: American Mathematical Society.

@@ Line 31: / Line 31: @@
 Köhler and Altmann (2000) considered the depth of embedding in the Susanne corpus and obtained the results presented in Table 1 and Fig. 1.
-Table 1
+<div align="center">[[Image:Tabelle1_DoSC.jpg]]</div>
 <div align="center">[[Image:Grafik1_DoSC.jpg]]</div>

Depth of syntactic constructions - Revision history

Ahans at 13:28, 27 June 2006

Ahans at 15:14, 17 June 2006