Synonymy

1. Problem and history

Two words are synonymous if they have the same meaning. Even if absolute synonymy is seldom, approximate synonymy is usual in specific contexts. Synonymy arises through (→) diversification of the meaning of words and can be eliminated by unification (cf. Altmann 1986).

From this point of view the problem has been analyzed merely by Wimmer and Altmann (2001a) who studied the synonymy in Italian and Ziegler (2001a) who studied it in German and English.

2. Hypothesis

The rise and elimination of synonyms is controled by a birth-and-death process.

3. Derivation

3.1. Wimmer-Altmann´s model

The dynamics of synonymy is a Poissonian birth-and-death process with constant birth (λ) and death rates (μ) respectively. Inserting them in the balancing equation we obtain

(1)$\lambda P_0 = \mu P_1 <math> (\lambda + \mu) P_x = \lambda P_{x+1}, \quad x=1,2,3,...$

Stepwise solution and setting q = λ/μ, (0 < q < 1) yields the geometric distribution

(2)$P_x = pq^{x-1}, \quad x=0,1,2,...$

Since words with 0 synonyms are not contained in the usual dictionary of synonyms, one either uses the 1-displaced geometric distribution which can be arrived at by a displacement in (1), i.e.

(3)$P_x= pq^{x-1}, \quad x=1,2,3$

or one takes these words with 0 synonymy from a usual but incommensurable dictionary. In that case it is advisable to modify (2) and use

(4)$P_x = \begin{cases} 1-\alpha, & x=0 \\ \alpha pq^{x-1}, & x=1,2,3,... \end{cases}$

Example: Synonymy in Italian

Wimmer and Altmann (2001a) took a random sample (15 pages) from the Italian dictionary of P. Stopelli, Sinonimi e Contrari con generici, Spezifici, Analoghi, Inversi. (Garzanti 1998) and obtained the distribution as presented in Table 1. Separartely they used the dictionary of P. Giovanelli, W. Frenzel, Langenscheidts Handwörterbuch Italienisch (Berlin, Langenscheid 1998) from wich thay sampled words with 0 synonyms (i.e. those not occurring in the dictionary of synonyms but laying between the synonyms on the given page). The results of fitting of (3) and (4) to these data are shown in Table 1 and Fig. 1.

Fig. 1. Fitting the modified geometric distribution to the data in Table 1

The fitting in both cases is very satisfactory.

3.2. Ziegler´s model

Ziegler (2001) ascertained that for German and English data the assumptions in 3.1 are not sufficient. Using the same process he postulated

$\lambda = a + bx\quad$

$\mu = x\quad$

and obtained the balancing equations in form

(5)$aP_0 = P_1\quad$

$(a+bx+x)P_x = [a+b(x-1)]P_{x-1}+(x+1)P_{x+1}, \quad x=1,2,3,...$

leading by stepwise addition of lines to

(6)$P_x= \frac{a+b(x-1)}{x}P_{x-1}$

Setting a/b = k and b = q one obtains

(7)$P_x = \frac{k+x-1}{x}qP_{x-1}$

resulting in the negative binomial distribution. Displacing it conventionally one step to the right one gets

(8)$P_x= {k+x-2 \choose x-1}p^k q^{x-1}, \quad x=1,2,3,...$

Example. Synonymy in German dictionary

Ziegler analyzed German data using Der Duden Bd. 8 (1997, second edition) and obtained results presented in Table 2 and Fig. 2. Since for x = 34 to x = 71 there are no observed cases, the only case in x = 72 was pooled with that of x = 33. The present results are slightly different from those in Ziegler (2001)

Fig. 2. Fitting the negative binomial distribution to the data in Table 2

Note. For English neither (4) nor (8) were sufficient, perhaps because of the extensive language mixture. Ziegler proposed the mixed negative binomial distribution.

4. Authors: G. Altmann

5. References

Der Duden Bd. 8 ($1997^2$). Duden. Die sinn- und sachverwandte Wörter. Synonymwörterbuch der deutschen Sprache. Mannheim: Dudenverlag.

Giovanelli, P., Frenzel, W. (1998). Langenscheidts Handwörterbuch Italienisch. Berlin: Langenscheid.

Stopelli, P. (1998). Sinonimi e contrari con generici, spezifici, analoghi, inversi. Milano: Garzanti.

The Nuttall (1$976^21$). The Nuttall dictionary of English synonyms and antonyms. Ed. by G.E. Christ. Ner York-London: Warne.

Wimmer, G., Altmann, G. (2001a). Two hypotheses on synonymy. In: Ondrejovič, S., Považaj, M. (eds.), Lexicographica ´99: 218-225. Bratislava: Veda.

Ziegler, A. (2001a). Zum Gesetz der Synonymie. Modellanpassungen im Deutschen und Englischen. In: Ondrejovič, S., Považaj, M. (eds.), Lexicographica ´99: 230-236 . Bratislava: Veda