Abstract
A long-standing problem in linguistics is how to define word. Recent research has focused on the incompatibility of diverse definitions, and the challenge of finding a definition that is crosslinguistically applicable. In this study I take a different approach, asking whether one structure is more word-like than another based on the concepts of predictability and information. I hypothesize that word constructions tend to be more “internally predictable” than phrase constructions, where internal predictability is the degree to which the entropy of one constructional element is reduced by mutual information with another element. I illustrate the method with case studies of complex verbs in German and Murrinhpatha, comparing verbs with selectionally restricted elements against those built from free elements. I propose that this method identifies an important mathematical property of many word-like structures, though I do not expect that it will solve all the problems of wordhood.
Funding source: Australian Research Council
Award Identifier / Grant number: DE180100872
Acknowledgments
This paper has benefited from discussion with Christian Döhler, Charles Kemp, William Lane, Frank Mollica, Nicholas Lester, Rachel Nordlinger, and Adam Tallman, as well as audiences at the University of Zurich Centre for Linguistics and the University of Melbourne Computational Cognitive Science lab. Further improvements were made thanks to the comments of two anonymous reviewers.
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Research funding: The research was funded by the Australian Research Council, grant number DE180100872.
Appendix: Sample size effects on entropy and internal predictability
Entropy estimates can be highly inaccurate with small samples, and this is an important issue for any corpus study of lexical items, which by Zipf’s law include many rare items. In this study the sample size effect is mitigated in two ways: firstly, but using the Chao-Shen entropy estimation method (Gotelli and Chao 2013), which corrects for small samples. Secondly, in the presentation of individual lexemes’ predictability measurements (Sections 6.1 and 7.1), I exclude lexemes with less than 10 corpus tokens.
In this Appendix I illustrate some effects of sample size on the estimation of complex verb entropy. I focus here on the German corpus data, which yielded a larger sample of 77,946 complex verb tokens. Comparing entropy estimates for smaller subsets of this data gives us some insight into the accuracy of the smaller Murrinhpatha sample, which consists of 6,041 complex verb tokens.
First, I show the effect of different sample sizes on estimating the preverb entropy of individual verb stems. This is done by drawing repeated independent samples from the full dataset.[19] Figure A1 shows particle entropy estimates for lexical stems appearing in the phrase construction, using the three stems illustrated in Table 6 of the main paper: arbeiten, streichen, werfen. Entropy estimates are on the y-axis, and sample size is on the x-axis (which is on a square-root scale). Cho-Shen entropy estimates are shown as heavier dots, and empirical entropy estimates as lighter crosses. For both methods, estimates have a high degree of variance with smaller samples, and gradually converge as the sample size increases. The Chao-Shen method both over- and under-estimates entropy in small samples, but importantly, estimates tend to cluster around the central value converged upon in larger samples. Empirical entropy estimates, on the other hand, systematically under-estimate entropy at smaller sample sizes.
Particle entropy estimates for three German verb stems, using different corpus sample sizes.
In my presentation of preverb predictability among individual verb stems (Sections 6.1 and 7.1), a minimal token threshold of 10 was selected to mitigate estimation inaccuracy, while also including as many verb stems as possible. As shown in Figure A1, Chao-Shen estimates with only 10 tokens can be somewhat inaccurate, though estimates cluster towards the true value. The three stems shown here are among those with higher token counts (between 50 and 300), but as is typical with Zipfian lexical distributions, many stems have far fewer tokens. Therefore, the preverb entropy estimates shown for individual verb stems in the main paper will have variable accuracy, according to token count, with N ≥ 10 set as a floor to avoid the most egregious errors.
Figure A2 shows prefix entropy estimates for three verb stems in the word-type construction. All have very low prefix entropy. At smaller sample sizes the figure shows some massive over-estimates, which occur when a small sample happens to include one of the rare prefix combinations. However, the vast majority of small-sample estimates are in fact zero, i.e., quite accurate. Over-plotting of points obscures the predominance of accurate estimates, but regression lines (dashed for Chao-Shen, solid for empirical) have been added to show the overall accuracy. The stem reichen only ever occurs with the prefix er- in our sample, and therefore all estimates are zero.
Prefix entropy estimates for three German verb stems, using different corpus sample sizes.
In the overall measures of construction type internal predictability (IP) (Figure 5 in the main article), all verb stems are included irrespective of token frequency. This gives a more complete picture of predictability in the construction type, since rare lexemes are an intrinsic part of corpus distributions. Importantly, IP is a weighted average across verb stems, and therefore considers token frequency (i.e., verb stem probability), in a way that is not evident in the individual lexeme figures. Highly frequent stems, with more accurate entropy estimates, have a greater influence on IP. Low-frequency stems, with less reliable entropy estimates, each have a very small influence on IP.
Finally, it is worth considering the effect of the total sample size on IP, especially since Murrinhpatha provided a much smaller sample. Figure A3 shows IP measures for different sized independent samples of the German complex verb dataset. Again, both Chao-Shen and empirical estimates are shown. Cho-Shen estimates (dots) converge to a stable value by around 10,000 complex verb tokens. Empirical estimates (crosses) overestimate IP, especially in the more unpredictable phrase construction. Given that 6,041 tokens were available for Murrinhpatha complex verbs, and assuming that the laws of sample size would apply similarly to Murrinhpatha as to German, we can see that Chao-Shen estimates for Murrinhpatha are likely to be accurate within a few percentage points.
Internal predictability estimates for German complex verb construction types, using different corpus sample sizes.
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