Journal of Logic, Language and Information

, Volume 21, Issue 4, pp 461-477

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Explaining Quantity Implicatures

  • Robert van RooijAffiliated withInstitute for Logic, Language and Computation, Universiteit van Amsterdam Email author 
  • , Tikitu de JagerAffiliated withInstitute for Logic, Language and Computation, Universiteit van Amsterdam


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.


Conversational implicatures Pragmatics Game theory