Abstract
A key fact about linguistic communication is that utterances are often produced imprecisely by speakers and interpreted imprecisely by listeners. Modeling imprecision is a particular challenge for computational pragmaticists working in the Rational Speech Act (RSA) framework (Frank and Goodman 2012; Goodman and Stuhlmüller 2013): a standard assumption of RSA models is that the speaker’s production choices are constrained to utterances that are true in a strict sense given the speaker’s intended meaning.
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Notes
- 1.
I’d like to express my gratitude to Christoph Hesse for reviewing my submission to this volume, as well as to Cleo Condoravdi, Judith Degen, and Zion Mengesha for insightful feedback and commentary on my analysis. I also gratefully acknowledge Judith Degen, Dan Lassiter, and the ALPS lab at Stanford for insightful discussion of earlier versions of this work. Finally, thank you to Nicole Gotzner and Uli Sauerland for the opportunity to contribute to this volume in honor of Stephanie Solt, who I’m fortunate to call a mentor, collaborator, and friend. All errors, inconsistencies, and shortcomings in this paper are entirely my own.
- 2.
- 3.
On an enriched version of this model, the \(L_0\) distribution is further modulated by a non-uniform prior over possible meanings.
- 4.
The reader familiar with RSA may note that the \(\alpha \) optimality parameter has been omitted from this definition. I will introduce an optimality parameter when I present my proposal. Excluding the optimality parameter at this stage has no bearing on the point I am making in this section, which is that standard RSA pragmatic speakers only produce utterances that are literally true given the intended meaning.
- 5.
Admittedly, it is a bit unnatural to produce The townspeople are asleep imprecisely in a context where there are only 10 townspeople. An imprecise production of (1) is almost certainly more felicitous when the speaker believes that 498/500 (or 4998/5000) of the townspeople are asleep. For simplicity and for illustrative purposes, I restrict myself to a small set of possible meanings.
- 6.
I computed these probabilities using M.H. Tessler’s rwebppl package, which provides an R interface to the probabilistic programming language WebPPL (Goodman and Stuhlmüller 2014). See https://github.com/mhtess/rwebppl. All code related to this paper can be accessed at https://github.com/bwaldon/rsaImprecision.
- 7.
What types of contexts permit speakers to relax their adherence to this maxim? As Lauer (2012) notes, ‘[the b]enefits of speaking loosely come in many forms’ (2012: 396). In particular, there are competing pressures on speakers to speak truthfully while also tailoring their utterances to meet contextual standards of relevance and to avoid prolixity (see also Krifka [2002] for discussion of the relationship between brevity and imprecision). Speakers can also leverage linguistic (im)precision to convey social meaning (Beltrama 2018; Beltrama and Burnett 2019). I will have relatively little to say about how interlocutors recognize that the context permits imprecision. Rather, my focus will be on modeling speaker production choices and listener inferences in contexts in which imprecision is mutually recognized to be licensed.
- 8.
This means that some utterances (incl. none-asleep, the-asleep, and all-asleep) will not have well-defined \(S_{PT}\) distributions in Model 1 because they are not asymmetrically entailed by other utterance alternatives.
- 9.
A similar model of an imprecise speaker is employed by Waldon and Degen (2020) to explain the tendency of some participants in truth-value judgment task experiments to endorse strictly false sentences of the form A and B in contexts where \(A \wedge \lnot B\) holds. The authors model truth-value judgment task behavior—e.g. the probability of endorsing a sentence in context as ‘Right’/‘True’—as a function of the probability of the sentence being produced in context by an RSA pragmatic speaker. By defining this speaker as an imprecise \(S_I\) speaker, the authors can model participants as having some expectation that A and B will be produced in \(A \wedge \lnot B\) contexts.
- 10.
For some recent experimental evidence that potentially complicates this intuition, see Ramotowska et al. (2020), who report the results of a truth value judgment task experiment in which participants evaluated sentences of the form Most of the Ps are Q given contextual knowledge that N% of the Ps are Q (where N ranged between 1 and 99). From their data, the authors estimate that for a minority of participants the threshold of proportion for most is slightly below 50%.
- 11.
You can think of these new utterances as corresponding to something like At least seven/eight/nine of the townspeople are asleep. I won’t wade into the longstanding debate as to whether or not numerals are semantically upper-bounded (see e.g. Bylinina and Nouwen [2020] for recent discussion). However, in order for this analysis to extend to imprecise interpretation of number words, one would have to commit to a lower-bounded semantics (so as to allow that sentences like Nine of the townspeople are asleep and Ten of the townspeople are asleep can overlap in propositional content). There are more challenges beyond this, including that although the imprecise \(L_1\) listener distribution over meanings given observation of N of the townspeople are asleep would have most of its mass at \(\mathbf{m _N}\), the left and right tails of the distribution would each be differently sensitive to the \(\alpha \) optimality parameter and the \(\beta \) imprecision function. A demonstration of this undesirable behavior is available in the GitHub repository (linked above). I’m grateful to Christoph Hesse for the discussion of this point.
- 12.
Similarly, in Sect. 4.1, we observed that adding more fine-grained alternatives to the context led to a decrease in the probability with which the-asleep was associated with meanings relatively far away from \(\mathbf{m} _{10}\). Compare Figs. 5 and 6: on Model 1 (with \(\alpha = 1\) and \(\beta \) defined as in 10), \(L_1(\mathbf{m _6}|{the-asleep})\) and \(L_1(\mathbf{m _7}|{the-asleep})\) are approximately 0.1. However, these values are much lower than 0.1 on Model 2 (the model with more alternatives) even when keeping \(\alpha \) and \(\beta \) constant. This suggests that, similar to Solt’s analysis, introducing fine-grained alternatives restricts the range of possible meanings with which the listener associates the imprecise speaker’s utterance.
- 13.
See footnote 11 above.
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Waldon, B. (2022). A Novel Probabilistic Approach to Linguistic Imprecision. In: Gotzner, N., Sauerland, U. (eds) Measurements, Numerals and Scales. Palgrave Studies in Pragmatics, Language and Cognition. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-73323-0_17
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