Quantity implicatures, exhaustive interpretation, and rational conversation
Quantity implicatures are inferences triggered by an utterance based on what other utterances a speaker could have made instead. Using ideas and formalisms from game theory, I demonstrate that these inferences can be explained in a strictly Gricean sense as *rational behavior*. To this end, I offer a procedure for constructing the context of utterance insofar as it is relevant for quantity reasoning as a game between speaker and hearer. I then give a new solution concept that improves on classical equilibrium approaches in that it uniquely selects the desired "empirically correct" play in these interpretation games by a chain of back-and-forth reasoning about players' behavior. To make this formal approach more accessible to a wider audience, I give a simple algorithm with the help of which the model's solution can be computed without having to do heavy calculations of probabilities, expected utilities and the like. This rationalistic approach subsumes and improves on recent exhaustivity-based approaches. It makes correct and uniform predictions for quantity implicatures of various epistemic varieties, free choice readings of disjunctions, as well as a phenomenon tightly related to the latter, namely so-called "simplification of disjunctive antecedents".
quantity implicature; exhaustive interpretation; game theory; iterated best response
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Journal doi: http://dx.doi.org/10.3765/sp