Modeling (im)precision in context:

Roland Mühlenbernd; Stephanie Solt

doi:10.1515/lingvan-2022-0035

Published by De Gruyter Mouton December 22, 2022

Modeling (im)precision in context

Roland Mühlenbernd and Stephanie Solt

From the journal Linguistics Vanguard

https://doi.org/10.1515/lingvan-2022-0035

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Abstract

Speakers’ choice between linguistic alternatives often depends on the situation, a prime example involving level of precision at which numerical information is communicated. We report on a production study in which participants report the time of an event in two different situations, and demonstrate that the results can be reproduced by a probabilistic game-theoretical model in which the speaker’s choice reflects a tradeoff between informativity, accuracy and hearer-oriented simplification. These findings shed light on the pragmatics of (im)precision, and the dynamics of situationally driven pragmatic variation more generally.

Keywords: pragmatic variation; probabilistic model; production study; rounding; time report

Corresponding author: Roland Mühlenbernd, Leibniz-Zentrum Allgemeine Sprachwissenschaft (ZAS), Berlin, Germany, E-mail: muehlenbernd@leibniz-zas.de

Funding source: Deutsche Forschungsgemeinschaft

Award Identifier / Grant number: SFB 1412, 416591334

Acknowledgments

We thank Heather Burnett, Manfred Krifka, Uli Sauerland and the audiences at the ZAS and Humboldt University for helpful discussion, and Alexandra Fossa and Hadewych Versteegh for assistance with the data analysis of the experimental data.

Research Funding: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – SFB 1412, 416591334.

Appendix A: Supplementary tables and figures

Table A.1:

The experimental sessions 1 and 2, the date when each took place, the number of participants, and links to the experiment, designed with LabVanced and stored at the LabVanced server. Of the 502 participants, 3 did not complete the experiment, and were excluded for analysis. Participants took on average 4.38 min for the whole session.

ID	Date	Participants	Link
1	May 3rd 2021	250	www.labvanced.com/player.html?id=22972
2	May 17th 2021	252	www.labvanced.com/player.html?id=23753

Table A.2:

Distribution of participants over 14 different conditions.

Situation	Information	Participants
Police context	8:30	32
Police context	8:30 ± 1	27
Police context	8:30 ± 2	28
Police context	8:30 ± 3	35
Police context	8:30 ± 4	29
Police context	8:30 ± 5	30
Police context	8:26–8:34	65
Neighbor context	8:30	31
Neighbor context	8:30 ± 1	32
Neighbor context	8:30 ± 2	35
Neighbor context	8:30 ± 3	31
Neighbor context	8:30 ± 4	32
Neighbor context	8:30 ± 5	32
Neighbor context	8:26 − 8:34	60

		499

Table A.3:

Categorization of reason(s) for choice (# of respondents; multiple categories possible).

Answer category	Police	Neighbor
Level of precision/detail	51	61
Accuracy/truthfulness	28	20
Possible lack of information	17	13
Possible misinformation	9	3
Safe choice	2	2
Hearer needs	19	13
Appropriateness for context	15	33
Speaker ease	7	22
Hearer ease	6	14
Habit/convention	35	52
How it sounds	2	7
Other/irrelevant	108	105

Total # of respondents	231	244

Table A.4:

Utterances v ∈ V , each with its corresponding core semantic meaning 〚 v 〛 as a subset of the temporal domain T, its roundness level r n d ( v ) , and a sample utterance. Here, utterances with value that are completely divisible by 15 have the highest roundness level of 2, remaining utterances with values that are divisible by 5 have a roundness level of 1, and all remaining utterances have a roundness level of 0; these correspond to distinct granularity levels in the temporal domain discussed in Krifka (2009).

v ∈ V	Core semantic meaning 〚v〛	rnd(v)	Sample utterance
v 25	{ 25 }	1	‘ … at 8:25.’
v 26	{ 26 }	0	‘ … at 8:26.’
v 27	{ 27 }	0	‘ … at 8:27.’
v 28	{ 28 }	0	‘ … at 8:28.’
v 29	{ 29 }	0	‘ … at 8:29.’
v 30	{ 30 }	2	‘ … at 8:30.’
v 31	{ 31 }	0	‘ … at 8:31.’
v 32	{ 32 }	0	‘ … at 8:32.’
v 33	{ 33 }	0	‘ … at 8:33.’
v 34	{ 34 }	0	‘ … at 8:34.’
v 35	{ 35 }	1	‘ … at 8:35.’
v a 25	{ 22,23,24,25,26,27,28 }	1	‘ … around 8:25.’
v a 30	{ 27,28,29,30,31,32,33 }	2	‘ … about 8:30.’
v a 35	{ 32,33,34,35,36,37,38 }	1	‘ … approximately at 8:35.’
v I n	{ 25,26,27,28,29,30,31,32,33,34,35 }	0	‘ … between 8:25 and 8:35.’

Figure A.1:

Images of the different clocks presenting the different information states.

Figure A.2:

Participant responses (absolute numbers) by information state in (a) police context and (b) neighbor context. ‘Other’ responses are those for which participants’ justifications indicated they had misread the clock face (e.g. reading 8:32 as 8:37 or incorrectly interpreting the approximate state 8:26–8:34 as representing an interval around 6 o’clock) or otherwise misunderstood the experimental task. These responses were excluded from further analysis and model fitting.

Figure A.3:

Normalized distribution of approximator term choices in each context. Here, ‘approx’ stands for ‘approximately’, and ‘just b/a’ stands for ‘just before’ and ‘just after’.

$Figure A.4: Mean square errors between an empirical production matrix and computationally reconstructed matrices over different parameter values for w R ${w}_{R}$ (x axis) and w A ${w}_{A}$ (y axis), left for police context, right for neighbor context. Mean square error values are coded from high value ≥ 0.0035 $\ge 0.0035$ (dark blue) down to 0.001 (dark red); color bar on the right. The juxtaposition of both heat maps shows that the optimal reconstruction of the ‘police context’ matrix involves a lower w R ${w}_{R}$ value and a higher w A ${w}_{A}$ value than the optimal reconstruction of the ‘neighbor context’ matrix.$

Figure A.4:

Mean square errors between an empirical production matrix and computationally reconstructed matrices over different parameter values for w R (x axis) and w A (y axis), left for police context, right for neighbor context. Mean square error values are coded from high value ≥ 0.0035 (dark blue) down to 0.001 (dark red); color bar on the right. The juxtaposition of both heat maps shows that the optimal reconstruction of the ‘police context’ matrix involves a lower w R value and a higher w A value than the optimal reconstruction of the ‘neighbor context’ matrix.

$Figure A.5: Juxtaposition of mean square error (left), Pearson correlation and goodness-of-fit value (right) for the optimal reconstruction of the police context matrix (blue bar), the neighbor context matrix (red bar) and for all data points of both matrices combined (across contexts, beige bar). The ’across context’ model assumes no difference of weights w R ${w}_{R}$ and w A ${w}_{A}$ across both contexts. It is optimal reconstruction achieves a clearly worse mean square error (about triple as high), as well as a worse Pearson correlation r $r$ and a worse goodness-of-fir value r 2 ${r}^{2}$ .$

Figure A.5:

Juxtaposition of mean square error (left), Pearson correlation and goodness-of-fit value (right) for the optimal reconstruction of the police context matrix (blue bar), the neighbor context matrix (red bar) and for all data points of both matrices combined (across contexts, beige bar). The ’across context’ model assumes no difference of weights w R and w A across both contexts. It is optimal reconstruction achieves a clearly worse mean square error (about triple as high), as well as a worse Pearson correlation r and a worse goodness-of-fir value r 2 .

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Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/lingvan-2022-0035).

Received: 2022-03-27

Accepted: 2022-09-26

Published Online: 2022-12-22