Length of syntactic constructions - Revision history

Ahans: Length of syntactic constructions: moved to Length of syntactic constructions

2006-07-25T11:27:28Z

Length of syntactic constructions: moved to Length of syntactic constructions

Altmann at 12:46, 24 July 2006

2006-07-24T12:46:18Z

Ahans at 13:36, 11 July 2006

2006-07-11T13:36:35Z

Ahans at 13:36, 11 July 2006

2006-07-11T13:36:17Z

Ahans at 13:35, 11 July 2006

2006-07-11T13:35:57Z

Rkoehler: Syntactic constructions: Length moved to Length of syntactic constructions:

2006-06-29T21:25:38Z

Syntactic constructions: Length moved to Length of syntactic constructions:

Ahans at 15:01, 17 June 2006

2006-06-17T15:01:59Z

New page

'''1. Problem and history'''

The length of a syntactic construction is defined as the number of terminal nodes belonging to it, while complexity (<math>\rightarrow</math>) is he number of its immediate constituents. These two properties are interrelated.

The first distribution models were proposed by Köhler and Altmann (2000), no further development is known. As can be seen, the result is a special case of length (<math>\rightarrow</math>) distributions.

'''2. Hypothesis'''

''The length of syntactic constructions abides by the positive negative binomial distribution''.

'''3. Derivation'''

The quantities necessary for the derivation are shown in the chapter “Syntactic structures: Complexity” (<math>\rightarrow</math>). Here the requirement minX = 0, because length depends on complexity and minX is given implicitely. Using the approach proposed for modeling complexity we obtain

(1)<math> P_x = \frac{max H + x}{x}\frac{E}{I(K)}P_{x-1}</math>.

Setting again maxH = k-1, E/I(K) = q (0 < q < 1) and solving (1) we obtain

(2)<math> P_x= {k+x-1 \choose x}\frac{p^k q^x}{1-p^k}, \quad x=1,2,3,... </math>

If maxH tends to -1, i.e. k <math>\rightarrow</math> 0, we obtain the logarithmic distribution

(3)<math> P_x= \frac{q^x}{-x \ln(1-q)}, \quad x=1,2,3,...</math>

but in particular cases it is necessary to modify the probability in x = 1 and one obtains the extended variants of (2) and (3), namely

(4)<math> P_x = \begin{cases} 1-\alpha, & x=1 \\ \alpha {k+x-2 \choose x-1}\frac{p^k q^x}{1-p^k}, & x=2,3,... \end{cases}</math>

(5)<math>P_x = \begin{cases} 1-\alpha, & x=1 \\ \frac{\alpha q^{x-1}}{-(x-1)\ln (1-q)}, & x=2,3,4,... \end{cases}</math>

Example: The length of syntactic constructions in the Susanne corpus
The result of fitting of the extended logarithmic distribution to the data in Susanne corpus are shown in Table 1 and Fig. 1 (Köhler, Altmann 2000).

Table 1
Fitting the extended logarithmic distribution to the data in Susanne corpus

Though the chi-square value is very high, the fit is satisfactory as shown by the value of C. The greatest divergence is in the middle range where one can observe strong fluctuation.

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

'''5. References'''

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

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−	'''4. Authors''': G. Altmann	+	'''4. Authors''': U. Strauss, G. Altmann

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	<div align="center">[[Image:Tabelle111_SCL.jpg]]</div>		<div align="center">[[Image:Tabelle111_SCL.jpg]]</div>
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	Though the chi-square value is very high, the fit is satisfactory as shown by the value of C. The greatest divergence is in the middle range where one can observe strong fluctuation.		Though the chi-square value is very high, the fit is satisfactory as shown by the value of C. The greatest divergence is in the middle range where one can observe strong fluctuation.

← Older revision		Revision as of 13:35, 11 July 2006
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	The result of fitting of the extended logarithmic distribution to the data in Susanne corpus are shown in Table 1 and Fig. 1 (Köhler, Altmann 2000).		The result of fitting of the extended logarithmic distribution to the data in Susanne corpus are shown in Table 1 and Fig. 1 (Köhler, Altmann 2000).

		+	<div align="center">[[Image:Tabelle111_SCL.jpg]]</div>

−	~~Table 1~~
−	~~Fitting the extended logarithmic distribution to the data in Susanne corpus~~

← Older revision	Revision as of 11:27, 25 July 2006
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-Though the chi-square value is very high, the fit is satisfactory as shown by the value of C. The greatest divergence is in the middle range where one can observe strong fluctuation.
+'''4. Authors''':  G. Altmann
 '''5. References'''
 '''Köhler, R., Altmann, G.''' (2000). Probability distributions of syntactic units and properties. ''J. of Quantitative Linguistics 7, 189-200''.

← Older revision	Revision as of 21:25, 29 June 2006
(No difference)