Abstract
We give derivations of two formal models of Gricean Quantity implicature and strong exhaustivity in bidirectional optimality theory and in a signalling games framework. We show that, under a unifying model based on signalling games, these interpretative strategies are game-theoretic equilibria when the speaker is known to be respectively minimally and maximally expert in the matter at hand. That is, in this framework the optimal strategy for communication depends on the degree of knowledge the speaker is known to have concerning the question she is answering. In addition, and most importantly, we give a game-theoretic characterisation of the interpretation rule Grice (formalising Quantity implicature), showing that under natural conditions this interpretation rule occurs in the unique equilibrium play of the signalling game.
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References
Benz, A., Jäger, G., van Rooij, R. (eds) (2006) Game theory and pragmatics. Palgrave McMillan, Basingstoke
Blutner R. (2000) Some aspects of optimality in natural language interpretation. Journal of Semantics 17: 189–216
Gärdenfors P. (2000) Conceptual spaces: The geometry of thought. Cambridge, Massachusetts
Gazdar G. (1979) Pragmatics. Academic Press, London
Grice, H. P. (1967). Logic and conversation. The William James lectures, delivered at Harvard University. Republished with revisions in Grice, 1989.
Horn, L. R. (1972). The semantics of logical operators in English. PhD thesis, Yale University.
Ifantidou E. (2001) Evidentials and relevance, volume 86 of pragmatics & beyond new series. John Benjamins, Amsterdam
Jäger G. (2007) The evolution of convex categories. Linguistics and Philosophy 30(5): 551–564
Keenan E. O. (1977) On the universality of conversational implicatures. In: Fasold R. W., Shuy R. W. (eds) Studies in language variation: Semantics, syntax, phonology, pragmatics, social situations, ethnographic approaches. Georgetown University Press, Washington, DC, pp 255–269
Levinson S. C. (2000) Presumptive meanings. The theory of generalized conversational implicatures. Cambridge, Massachusetts
Lewis D. K. (1969) Convention. Harvard University Press, Cambridge
Parikh P. (2001) The use of language. csli Publications, Stanford, California
Sauerland U. (2004) Scalar implicatures in complex sentences. Linguistics and Philosophy 27: 367–391
Schulz K., van Rooij R. (2006) Pragmatic meaning and non-monotonic reasoning: The case of exhaustive interpretation. Linguistics and Philosophy 29: 205–250
Spector, B. (2003). Scalar implicatures: Exhaustivity and Gricean reasoning? In B. ten Cate (Ed.), Proceedings of the eighth ESSLLI student session, Vienna, Austria.
Thijsse E. (1983) On some proposed universals of natural language. In: ter Meulen A. G. B. (ed.) Studies in modeltheoretic semantics. Foris Publications, Dordrecht, pp 19–36
Van Benthem J. F. A. K. (1986) Essays in logical semantics. Reidel, Dordrecht
Van Rooij R., Schulz K. (2004) Exhaustive interpretation of complex sentences. Journal of Logic, Language and Information 13: 491–519
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van Rooij, R., de Jager, T. Explaining Quantity Implicatures. J of Log Lang and Inf 21, 461–477 (2012). https://doi.org/10.1007/s10849-012-9163-3
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DOI: https://doi.org/10.1007/s10849-012-9163-3