Discourse-Level Implicature: A Case for QUD

Abstract

This article argues that multisentence discourses give rise to Gricean quantity implicatures that go beyond the mere sum of the implicatures of the sentences they consist of. We formulate two theories of discourse-level implicature: the null theory, which only has a mechanism for sentence-level implicature and does not rely on any specific notion of discourse structure, and a theory that assumes that discourse is hierarchically structured by Questions Under Discussion (QUD) and that QUDs can guide the derivation of quantity implicatures at all levels of discourse structure. In two experiments using the inference task paradigm and focusing on sequences of sentences with contrastive topic, the QUD-based theory is shown to make more accurate predictions than the null theory. This finding provides additional motivation for the QUD-based approach to discourse structure.

Acknowledgment

We owe thanks to many people for discussing theoretical issues as well as the experimental design with us. We are especially grateful to Anton Benz, Dagmar Bittner, Bernhard Fisseni, Natalia Gagarina, Clemens Mayr, Edgar Onea, and Uli Sauerland. We also thank the audiences at the workshop “Questions in Discourse” at the annual meeting of the DGfS 2012 in Frankfurt/Main and at the Workshop “Information, discourse structure and levels of meaning (IDL12) 2012” in Barcelona as well as the anonymous reviewers of this article for their helpful comments. We particularly thank Felix Golcher for his assistance with the statistics.

Notes

¹ Of course, there are other kinds of evidence for (not necessarily QUD-based) discourse structure.

² There are more constraints on alternative sets that have been proposed in the literature, including contrastivity (Zeevat, 2004; Büring, 2008), availability (Geurts, 2010) and relative complexity (Fox & Katzir, 2011), their role, however is not discussed here.

³Klaus andMartha in (8) could also be marked as contrastive topics. However, this does not change anything in the analysis of this example assuming that only focus alternatives, and not topic alternatives are used in quantity implicature derivation.

⁵ The question What did Klaus and Martha eat? is ambiguous between a reading where the speaker wants to know what the group of individuals, consisting of Klaus and Martha, ate, and a reading where for each of Klaus and Martha, the speaker wants to know what he or she ate (cf. Krifka, 2001). In the first case, the set of QUD alternatives follows the pattern: ‘Klaus and Martha ate 2 apples,’ ‘Klaus and Martha ate 4 bananas,’ ‘Klaus and Martha ate…,’ etc. In the second case alternatives of the from ‘Klaus ate X’ and ‘Martha ate X’ are also included. The latter is equivalent to the set of alternatives of the question Who ate what? where the who-variable is restricted to the set of Klaus and Martha.

⁶ Another theoretical possibility is that the fronted noun bears a second narrow focus, giving rise to a double focus construction. In that case, both the fruit type variable and the number of pieces variable participate in the generation of focus alternatives at sentence level, so a sentence like (16) is predicted to implicate that Klaus did not eat any other number of any other fruit (in particular, no pears) even in the null theory. Intonation can disambiguate between CT+F and F+F structures, but it was absent in our experiments because we used written stimuli. Nevertheless, our final results suggest that CT+F must have been the preferred reading in our experimental materials, cf. discussion in fn. 8.

⁷ Fisseni (2010) tried to elicit exhaustivity inferences in a number of experimental designs. In general, the study suggests that exhaustivity is difficult to elicit. However, the designs where the alternatives for exhaustivity were explicitly given measured relatively higher numbers of exhaustivity inferences. With this potential problem in mind, we tried to maximize our chances to detect any exhaustivity inferences at all. This is why we introduced the alternative sets explicitly in the context, and this is also one of the reasons for using the inference task paradigm, which has been argued to push up the numbers of quantity implicatures (see Geurts & Pouscoulous, 2009).

⁸ 28.65% might still be seen as a rather high number given that the theories predict no exhaustivity at all in this condition. A possible explanation is that in a certain percentage of the cases the participants could have construed the fronted expression in the critical sentences as a focus rather than a contrastive topic, see fn. 6 on the double focus reading. At the same time, the fact that we found any effects at all suggests that the participants did not uniformly assume a double focus structure, which would have led to an equally high number of yes-responses to the exhaustivity inference in all four conditions. In other words, the participants must have assumed the CT+F reading in the +top condition frequently enough, so the fact that we used written materials without intonation (which would have disambiguated between F+F and CT+F structures) was not a problem.

Additional information

Funding

This research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant no. BE 4348/2-1, and the Emerging Group Dynamic Structuring in Language and Communication funded through the Institutional Strategy of the University of Cologne (ZUK 81/1).