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Exhaustivity Through the Maxim of Relation

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New Frontiers in Artificial Intelligence (JSAI-isAI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8417))

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Abstract

I show that the exhaustive interpretation of answers can be explained as a conversational implicature through the Maxim of Relation, dealing with the problematic epistemic step (Sauerland 2004). I assume a fairly standard Maxim of Relation, that captures the same intuition as Roberts’ (1996) contextual entailment. I show that if a richer notion of meaning is adopted, in particular that of attentive semantics (Roelofsen 2011), this Maxim of Relation automatically becomes strong enough to enable exhaustivity implicatures. The results suggest that pragmatic reasoning is sensitive not only to the information an utterance provides, but also to the possibilities it draws attention to. Foremost, it shows that exhaustivity implicatures can be genuine conversational implicatures.

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Notes

  1. 1.

    For brevity, I will typically use the word ‘know’ (and, likewise, ‘knowledge’) as if saying ‘taking oneself to know’, i.e., without requiring the usual factivity associated with knowledge as being ‘true belief’.

  2. 2.

    Groenendijk and Stokhof [10] already argued that exhaustivity cannot be derived through the Maxim of Quantity alone. After all, the Quantity implicature says ‘this is as informative as I can safely be’, hence it can never be used to strengthen what is said, as is required for the epistemic step. The contrast in (2) supports this view from a different angle: it’s not only quantity of information that matters.

  3. 3.

    The difference between positively and negatively exhaustive answers fades if the question under discussion is a partition. Given Groenendijk and Stokhof’s argument, I take this as strong evidence that, in general, questions (at least those in response to which a non-exhaustive answer would implicate exhaustivity) are not partitions; i.e., they have existential force, i.e., draw attention to their mention-some answers, rather than universal force.

  4. 4.

    This shows that, in this case, the Relation implicature in fact clashes with the Quantity implicature: for if the speaker really knows whether John was at the party, then why didn’t she just say so? As a consequence, the example will likely trigger additional implicatures to explain this clash, e.g., that the speaker wants to test the hearer’s knowledge. (Understandably, therefore, the example under discussion is more natural with a final rising pitch contour, which has been argued to convey uncertain relevance/relatedness [18].) Regardless of this, the example suffices for merely illustrating how the Maxim of Relation works.

  5. 5.

    The speaker can be competent in two ways, and in the case of exhaustivity, the Quality and Quantity implicatures together settle how (something which did not happen in the rainy party example). This shows that, as mentioned above, it would be too strict to require that the hearer already knows how a response is related to the question; in the case of exhaustivity, the Quality and Quantity implicatures enable her to figure it out.

  6. 6.

    In the future I hope to give such general descriptions of the Relation implicature also for cases where the response is any (potentially non-singleton) subset of the question, as these are all and only the cases that may yield exhaustivity implicatures. However, so far the results for such question-response pairs have not turned out any more readable than the general characterisation in (10), and I will omit them.

  7. 7.

    This possible objection was brought to my attention by Donka Farkas.

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Acknowledgments

I am grateful to Jeroen Groenendijk, Floris Roelofsen, Donka Farkas, Kai von Fintel, Chris Cummins, the audiences of SPE6 (St. Petersburg), S-Circle (UC Santa Cruz), ESSLLI Student Session 2013 (Düsseldorf), LIRA (Amsterdam), TbiLLC 2013 (Gudauri) and many anonymous reviewers for very helpful comments. Financial support from the Netherlands Organisation for Scientific Research is gratefully acknowledged.

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  1. Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands

    Matthijs Westera

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  1. Seikei University, Musashino-shi, Tokyo, Japan

    Yukiko Nakano

  2. National Institute of Informatics Research Division, Tokyo, Japan

    Ken Satoh

  3. Ochanomizu University, Tokyo, Japan

    Daisuke Bekki

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Westera, M. (2014). Exhaustivity Through the Maxim of Relation. In: Nakano, Y., Satoh, K., Bekki, D. (eds) New Frontiers in Artificial Intelligence. JSAI-isAI 2013. Lecture Notes in Computer Science(), vol 8417. Springer, Cham. https://doi.org/10.1007/978-3-319-10061-6_10

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  • DOI: https://doi.org/10.1007/978-3-319-10061-6_10

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