Explaining quantity implicatures

We give derivations of two formal models of Gricean Quantity1 implicature and strong exhaustivity (Van Rooij and Schulz, 2004; Schulz and Van Rooij, 2006), 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 Quantity1 implicature), showing that under natural conditions this interpretation rule occurs in the unique equilibrium play of the signalling game.

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