Elamur Research⌕
☰
home / papers / 2011 / Quantity implicatures, exhaustive interpretation, and rational conversation

Quantity implicatures, exhaustive interpretation, and rational conversation

Paper · 2011 · Michael Franke

Summary

The paper asks whether quantity implicatures can be derived in a strictly Gricean way, as the outcome of rational behaviour between speaker and hearer. An example is reading "some" as "not all". Franke proposes the iterated best response (ibr) model, which has two parts. The first is a fixed recipe that turns a target utterance and its alternatives into a signaling game. In that game, states group together worlds that agree on the truth of every alternative. The speaker knows the actual state, and both players want the hearer to identify it. The second part is a solution concept. Starting from literal truth, the players take turns computing best responses to each other's previous behaviour until the process stabilises. This picks out one intuitively correct outcome, where classical equilibrium notions allow many. A simple algorithm lets readers compute the result without working through expected-utility calculations. The model covers several epistemic kinds of quantity implicature, free choice readings of disjunction under existential modals, and simplification of disjunctive antecedents. It also improves on exhaustivity-based theories while giving them a rational foundation. The result matters because it links formal pragmatics back to Grice's idea of conversation as rational action.

Key points

  • The paper is published in Semantics & Pragmatics, vol. 4, article 1 (82 pages, 2011). Its model is called ibr (iterated best response).
  • It separates four strengths of quantity inference:
    • the general epistemic one (¬Bel_S "all"),
    • the strong epistemic one (Bel_S ¬"all"),
    • the weak epistemic one (speaker uncertain about "all"),
    • the base-level one (¬"all").
  • Theorem 3: in finite games of pure cooperation (U_S = U_R), every ibr sequence reaches a fixed point. The proof shows that expected gain never decreases along the sequence.
  • Theorem 4: under two conditions on interpretation games (C1, C2), any ibr fixed point gives rise to a perfect Bayesian equilibrium. Messages the hearer does not expect ("surprise messages") are interpreted with a uniform posterior over their literal meaning.
  • The model is close to, though not generally equivalent to, iterated exhaustive interpretation. Simple implicatures follow from rational interpretation of literal meaning alone, without needing a speaker quantity maxim.

Interesting ideas

  • I1. The context is built automatically from the alternatives, with no hand-chosen states: each state is the set of worlds that give all alternative utterances the same truth values. This keeps the model falsifiable and mechanical.
  • I2. Pragmatic reasoning is grounded in literal semantics and then refined step by step. Each player responds optimally to the other's previous strategy, which makes every inference step inspectable.
  • I3. The paper gives a fallback for unexpected input: a message nobody would send under the current strategy reverts to its literal meaning, with no preference among its states. This avoids inventing interpretations.
  • I4. A monotonicity argument guarantees termination: shared payoff can only rise along the iteration, and the game is finite, so the procedure must stop.
  • I5. The paper distinguishes how strong an inference is: the speaker not believing X, the speaker believing not-X, or not-X being true. This avoids collapsing different conclusions into one.

For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

  • I1 (frames): crate prag could build its implicature candidate space from the truth-value patterns of a sentence's scale-mates (some/all, or/and), so that every derived implicature traces back to an explicit table.
  • I2 (frames): implicature in prag can be modelled as a few explicit rounds of hearer and speaker tables over UD-derived literal meanings. Each round would be logged as part of the explanation.
  • I3 (world): when a sentence fits no expected pattern, the world builder should store only its literal content, without enriching it, and mark it as uncertain.
  • I4 (learn): self-play and repair-rule loops could carry a similar monotone objective, which would give a provable stopping condition and a sanity check.
  • I5 (answer): QA over fables could label answers derived from implicature with their epistemic strength, keeping "the narrator does not claim all" separate from "not all".

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓University of TübingenTübingen · Germany30 works · 40,834 citations

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 9,085 worksArtificial Intelligence · 8,888 worksArts and Humanities · 9,296 worksLanguage and Linguistics · 9,206 works

🧭 Topics 1Research subjects and languages the work is about.Implicature · 72 works

Cite

Cite as Michael Franke. 2011. Quantity implicatures, exhaustive interpretation, and rational conversation. Semantics and Pragmatics.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.3765/sp.4.1

@article{franke2011quantity,
  title = {{Quantity implicatures, exhaustive interpretation, and rational conversation}},
  author = {Michael Franke},
  journal = {Semantics and Pragmatics},
  year = {2011},
  doi = {10.3765/sp.4.1},
  url = {https://doi.org/10.3765/sp.4.1}
}

References

76 references, 0 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

  1. Allott, Nicholas. 2006. Game theory and communication. In Anton Benz, Gerhard Jäger & Robert van Rooij (eds.), Game theory and pragmatics, 123–151. Basingstoke and New York: Palgrave Macmillan. ↗
  2. Alonso-Ovalle, Luis. 2005. Distributing the disjuncts over the modal space. In Leah Bateman & Cherlon Ussery (eds.), Proceedings of the North East Linguistics Society (NELS) 35, Amherst, MA: GLSA. find
  3. Alonso-Ovalle, Luis. 2008. Innocent exclusion in an alternative-semantics. Natural Language Semantics 16(2). 115–128. doi:10.1007/s11050-008-9027-1. ↗
  4. Asher, Nicholas & Daniel Bonevac. 2005. Free choice permission is strong permission. Synthese 145(3). 303–323. doi:10.1007/s11229-005-6196-z. ↗
  5. Atlas, Jay David & Stephen Levinson. 1981. It-clefts, informativeness, and logical form. In Peter Cole (ed.), Radical pragmatics, 1–61. New York: Academic Press. find
  6. Bach, Kent. 2006. The top 10 misconceptions about implicature. In Betty Birner & Gregory Ward (eds.), Drawing the boundaries of meaning: Neo-Gricean studies in pragmatics and semantics in honor of Laurence R. Horn (Studies in Language Companion Series 80), 21–30. Amsterdam and Philadelphia, PA: John Benjamins. ↗
  7. Barker, Chris. 2010. Free choice permission as resource-sensitive reasoning. Semantics & Pragmatics 3(10). 1–38. doi:10.3765/sp.3.10. ↗
  8. Benz, Anton. 2006. Utility and relevance of answers. In Anton Benz, Gerhard Jäger & Robert van Rooij (eds.), Game theory and pragmatics, 195–219. Basingstoke and New York: Palgrave Macmillan. ↗
  9. Benz, Anton, Gerhard Jäger & Robert van Rooij (eds.). 2006. Game theory and pragmatics. Basingstoke and New York: Palgrave Macmillan. ↗
  10. Benz, Anton & Robert van Rooij. 2007. Optimal assertions and what they implicate. Topoi 26(1). 63–78. doi:10.1007/s11245-006-9007-3. ↗
  11. Camerer, Colin F. 2003. Behavioral game theory: Experiments in strategic interaction. Princeton, NJ: Princeton University Press. find
  12. Camerer, Colin F., Teck-Hua Ho & Juin-Kuan Chong. 2004. A cognitive hierarchy model of games. The Quarterly Journal of Economics 119(3). 861–898. doi:10.1162/0033553041502225. ↗
  13. Chapman, Siobhan. 2005. Paul Grice, philosopher and linguist. New York: Palgrave Macmillan. find
  14. Chemla, Emmanuel. 2009. Universal implicatures and free choice effects: Experimental data. Semantics & Pragmatics 2(2). 1–33. doi:10.3765/sp.2.2. ↗
  15. Chierchia, Gennaro. 2004. Scalar implicatures, polarity phenomena and the syntax/pragmatics interface. In Adriana Belletti (ed.), Structures and beyond (The Cartography of Syntactic Structures 3), 39–103. Oxford: Oxford University Press. ↗
  16. Chierchia, Gennaro, Danny Fox & Benjamin Spector. 2008. The grammatical view of scalar implicatures and the relationship between semantics and pragmatics. Unpublished manuscript. find
  17. Chierchia, Gennaro, Danny Fox & Benjamin Spector. 2009. Hurford’s constraint and the theory of scalar implicatures. In Paul Egré & Giorgio Magri (eds.), Presuppositions and implicatures. Proceedings of the MIT-Paris workshop (MIT Working Papers in Linguistics 60), http://semanticsarchive.net/ Archive/mE2OGIzY/HCChierchiaFoxSpector.pdf. ↗
  18. Cho, In-Koo & David M. Kreps. 1987. Signaling games and stable equilibria. The Quarterly Journal of Economics 102(2). 179–221. doi:10.2307/1885060. ↗
  19. Crawford, Vincent P. 2007. Let’s talk it over: Coordination via preplay communication with level-k thinking. Unpublished manuscript. find
  20. Crawford, Vincent P. & Nagore Iriberri. 2007. Fatal attraction: Salience, naïveté, and sophistication in experimental “hide-and-seek” games. The American Economic Review 97(5). 1731–1750. doi:10.1257/aer.97.5.1731. ↗
  21. Farrell, Joseph. 1993. Meaning and credibility in cheap-talk games. Games and Economic Behavior 5(4). 514–531. doi:10.1006/game.1993.1029. ↗
  22. Farrell, Joseph & Matthew Rabin. 1996. Cheap talk. The Journal of Economic Perspectives 10(3). 103–118. http://www.jstor.org/stable/2138522. ↗
  23. Fine, Kit. 1975. Critical notice: Counterfactuals. Mind 84(1). 451–458. doi:10.1093/mind/LXXXIV.1.451. ↗
  24. Fox, Danny. 2007. Free choice and the theory of scalar implicatures. In Uli Sauerland & Penka Stateva (eds.), Presupposition and implicature in compositional semantics, 71–120. Hampshire: Palgrave Macmillan. ↗
  25. Fox, Danny & Benjamin Spector. 2009. Economy and embedded exhaustification. Handout for a talk given at Cornell University. http://web.mit.edu/ linguistics/people/faculty/fox/Fox_Spector_Cornell.pdf. ↗
  26. Franke, Michael. 2009. Signal to act: Game theory in pragmatics. Amsterdam: Universiteit van Amsterdam dissertation. find
  27. Franke, Michael. 2010. Semantic meaning and pragmatic inference in non-cooperative conversation. In Thomas Icard & Reinhard Muskens (eds.), Interfaces: Explorations in logic, language and computation (Lecture Notes in Artificial Intelligence 6211/2010), 13–24. Berlin and Heidelberg: Springer-Verlag. doi:10.1007/978-3-642-14729-6_2. ↗
  28. Gazdar, Gerald. 1979. Pragmatics: Implicature, presupposition, and logical form. New York: Academic Press. find
  29. Geurts, Bart. 2005. Entertaining alternatives: Disjunctions as modals. Natural Language Semantics 13(4). 383–410. doi:10.1007/s11050-005-2052-4. ↗
  30. Geurts, Bart. 2010. Quantity implicatures. Cambridge: Cambridge University Press. find
  31. Geurts, Bart & Nausicaa Pouscoulous. 2009a. Embedded implicatures?!? Semantics & Pragmatics 2(4). 1–34. doi:10.3765/sp.2.4. ↗
  32. Geurts, Bart & Nausicaa Pouscoulous. 2009b. Free choice for all: A response to Emmanuel Chemla. Semantics & Pragmatics 2(5). 1–10. doi:10.3765/sp.2.5. ↗
  33. Grafen, Alan. 1990. Biological signals as handicaps. Journal of Theoretical Biology 144(4). 517–546. doi:10.1016/S0022-5193(05)80088-8. ↗
  34. Grice, Paul Herbert. 1975. Logic and conversation. In Peter Cole & Jerry L. Morgan (eds.), Speech acts (Syntax and Semantics 3), 41–58. New York: Academic Press. ↗
  35. Groenendijk, Jeroen & Martin Stokhof. 1984. Studies in the semantics of questions and the pragmatics of answers. Amsterdam: Universiteit van Amsterdam dissertation. find
  36. Ho, Teck-Hua, Colin Camerer & Keith Weigelt. 1998. Iterated dominance and iterated best response in experimental ‘p-beauty contests’. The American Economic Review 88(4). 947–969. find
  37. Horn, Laurence R. 1972. On the semantic properties of logical operators in English. Los Angeles: University of California, Los Angeles dissertation. find
  38. Horn, Laurence R. 1984. Towards a new taxonomy for pragmatic inference: Q-based and R-based implicature. In Deborah Shiffrin (ed.), Meaning, form, and use in context, 11–42. Washington: Georgetown University Press. find
  39. Horn, Laurence R. 1989. A natural history of negation. Chicago: Chicago University Press. find
  40. Jäger, Gerhard. 2007. The evolution of convex categories. Linguistics and Philosophy 30(5). 551–564. doi:10.1007/s10988-008-9024-3. ↗
  41. Jäger, Gerhard & Christian Ebert. 2009. Pragmatic rationalizability. In Arndt Riester & Torgrim Solstad (eds.), Proceedings of Sinn und Bedeutung 13, 1–15. de Jager, Tikitu & Robert van Rooij. 2007. Explaining quantity implicatures. In Proceedings of the 11th conference on theoretical aspects of rationality and knowledge (TARK), 193–202. New York: Association for Computing Machinery. doi:10.1145/1324249.1324276. ↗
  42. Kamp, Hans. 1973. Free choice permission. Proceedings of the Aristotelian Society 74. 57–74. http://www.jstor.org/stable/4544849. ↗
  43. Kamp, Hans. 1978. Semantics versus pragmatics. In Franz Guenthner & Siegfried Josef Schmidt (eds.), Formal semantics and pragmatics for natural languages, 255–287. Dordrecht: Reidel. ↗
  44. Katzir, Roni. 2007. Structurally-defined alternatives. Linguistics and Philosophy 30(6). 669–690. doi:10.1007/s10988-008-9029-y. ↗
  45. Klinedinst, Nathan. 2006. Plurality and possibility. Los Angeles: University of California, Los Angeles dissertation. find
  46. Kratzer, Angelika. 1981. Partition and revision: The semantics of counterfactuals. Journal of Philosophical Logic 10(2). 201–216. doi:10.1007/BF00248849. ↗
  47. Kratzer, Angelika & Junko Shimoyama. 2002. Indeterminate pronouns: The view from Japanese. In Yukio Otsu (ed.), Proceeding of the 3rd Tokyo conference on psycholinguistics, 1–25. van Kuppevelt, Jan. 1996. Inferring from topics: Scalar implicatures as topic-dependent inferences. Linguistics and Philosophy 19(4). 393–443. doi:10.1007/BF00630897. ↗
  48. Levinson, Stephen C. 1983. Pragmatics. Cambridge: Cambridge University Press. find
  49. Levinson, Stephen C. 2000. Presumptive meanings: The theory of generalized conversational implicature. Cambridge, MA: MIT Press. ↗
  50. Lewis, David. 1969. Convention: A philosophical study. Cambridge, MA: Harvard University Press. find
  51. Lewis, David. 1973. Counterfactuals. Cambridge, MA: Harvard University Press. find
  52. Matsumoto, Yo. 1995. The conversational condition on Horn scales. Linguistics and Philosophy 18(1). 21–60. doi:10.1007/BF00984960. ↗
  53. McClure, William. 2000. Using Japanese—a guide to contemporary usage. Cambridge: Cambridge University Press. find
  54. McKay, Thomas & Peter van Inwagen. 1977. Counterfactuals with disjunctive antecedents. Philosophical Studies 31(5). 353–356. doi:10.1007/BF01873862. ↗
  55. Merin, Arthur. 1992. Permission sentences stand in the way of boolean and other lattice-theoretic semantices. Journal of Semantics 9(2). 95–162. doi:10.1093/jos/9.2.95. ↗
  56. Mühlenbernd, Roland. 2009. Kommunikationsmodell für den Entwick-lungsprozess von Implikaturen: University of Bielefeld MA thesis. find
  57. Nute, Donald. 1975. Counterfactuals and the similarity of worlds. Journal of Philosophy 72(21). 773–778. doi:10.2307/2025340. ↗
  58. Parikh, Prashant. 1991. Communication and strategic inference. Linguistics and Philosophy 14(5). 473–514. doi:10.1007/BF00632595. ↗
  59. Parikh, Prashant. 2001. The use of language. Stanford, CA: CSLI Publications. find
  60. Rabin, Matthew. 1990. Communication between rational agents. Journal of Economic Theory 51(1). 144–170. doi:10.1016/0022-0531(90)90055-O. van Rooij, Robert. 2000. Permission to change. Journal of Semantics 17(2). 119–143. doi:10.1093/jos/17.2.119. van Rooij, Robert. 2003. Questioning to resolve decision problems. Linguistics and Philosophy 26(6). 727–763. doi:10.1023/B:LING.0000004548.98658.8f. van Rooij, Robert. 2004. Signalling games select horn-strategies. Linguistics and Philosophy 27(4). 493–527. doi:10.1023/B:LING.0000024403.88733.3f. van Rooij, Robert. 2006. Free choice counterfactual donkeys. Journal of Semantics 23(4). 383–402. doi:10.1093/jos/ffl004. van Rooij, Robert. 2008. Games and quantity implicatures. Journal of Economic Methodology 15(3). 261–274. doi:10.1080/13501780802321376. van Rooij, Robert. 2010. Conjunctive interpretation of disjunction. Semantics & Pragmatics 3(11). 1–28. doi:10.3765/sp.3.11. van Rooij, Robert & Katrin Schulz. 2004. Exhaustive interpretation of complex sentences. Journal of Logic, Language and Information 13(4). 491–519. doi:10.1007/s10849-004-2118-6. van Rooij, Robert & Katrin Schulz. 2006. Only: Meaning and implicatures. In Maria Aloni, Alistair Butler & Paul Dekker (eds.), Questions in dynamic semantics (Current Research in the Semantics/Pragmatics Interface 17), 193–223. Amsterdam and Singapore: Elsevier. ↗
  61. Ross, Alf. 1944. Imperatives and logic. Philosophy of Science 11(1). 30–46. doi:10.1086/286823. ↗
  62. Russell, Benjamin. 2006. Against grammatical computation of scalar implicatures. Journal of Semantics 23(4). 361–382. doi:10.1093/jos/ffl008. ↗
  63. Sauerland, Uli. 2004. Scalar implicatures in complex sentences. Linguistics and Philosophy 27(3). 367–391. doi:10.1023/B:LING.0000023378.71748.db. ↗
  64. Schulz, Katrin. 2005. A pragmatic solution for the paradox of free choice permission. Synthese 147(2). 343–377. doi:10.1007/s11229-005-1353-y. ↗
  65. Schulz, Katrin & Robert van Rooij. 2006. Pragmatic meaning and non-monotonic reasoning: The case of exhaustive interpretation. Linguistics and Philosophy 29(2). 205–250. doi:10.1007/s10988-005-3760-4. ↗
  66. Simons, Mandy. 2005. Dividing things up: The semantics of or and the modal/or interaction. Natural Language Semantics 13(3). 271–316. doi:10.1007/s11050-004-2900-7. ↗
  67. Spector, Benjamin. 2006. Scalar implicatures: Exhaustivity and Gricean reasoning. In Maria Aloni, Alistair Butler & Paul Dekker (eds.), Questions in dynamic semantics, 229–254. Amsterdam and Singapore: Elsevier. find
  68. Spector, Benjamin. 2007. Aspects of the pragmatics of plural morphology: On higher-order implicatures. In Uli Sauerland & Penka Stateva (eds.), Presupposition and implicature in compositional semantics, 243–281. Basingstoke and New York: Palgrave Macmillan. ↗
  69. Spence, Andrew Michael. 1973. Job market signaling. Quarterly Journal of Economics 87(3). 355–374. doi:10.2307/1882010. ↗
  70. Stalnaker, Robert. 1968. A theory of conditionals. In Nicholas Rescher (ed.), Studies in logical theory, 98–112. Oxford: Oxford University Press. ↗
  71. Stalnaker, Robert. 1998. Belief revision in games: Forward and backward induction. Mathematical Social Sciences 36(1). 31–56. doi:10.1016/S0165-4896(98)00007-9. ↗
  72. Stalnaker, Robert. 2006. Saying and meaning, cheap talk and credibility. In Anton Benz, Gerhard Jäger & Robert van Rooij (eds.), Game theory and pragmatics, 83–100. Basingstoke and New York: Palgrave Macmillan. von Stechow, Arnim & Thomas Ede Zimmermann. 1984. Term answers and contextual change. Linguistics 22(1). 3–40. doi:10.1515/ling.1984.22.1.3. ↗
  73. Swanson, Eric. 2010. Structurally defined alternatives and lexicalizations of XOR. Linguistics and Philosophy 33(1). 31–36. doi:10.1007/s10988-010-9074-1. ↗
  74. Veltman, Frank. 1985. Logics for conditionals. Amsterdam: Universiteit van Amsterdam dissertation. find
  75. Warmbrōd, Ken. 1981. Counterfactuals and substitution of equivalent antecedents. Journal of Philosophical Logic 10(2). 267–289. doi:10.1007/BF00248853. von Wright, Georg Henrik. 1951. Deontic logic. Mind 60(237). 1–15. doi:10.1093/mind/LX.237.1. von Wright, Georg Henrik. 1968. An essay on deontic logic and the theory of action. Amsterdam: North-Holland Publishing Company. ↗
  76. Zimmermann, Thomas Ede. 2000. Free choice disjunction and epistemic possibility. Natural Language Semantics 8(4). 255–290. doi:10.1023/A:1011255819284. Michael Franke Seminar für Sprachwissenschaft Universität Tübingen Wilhelmstraße 19 72074 Tübingen michael.franke@uni-tuebingen.de ↗

Updated

↑ back to top

This page in Markdown → https://md.research.elamur.ai/free/en/papers/franke-2011-quantity-implicatures-exhaustive-interpretation-rational/