Quantity implicatures, exhaustive interpretation, and rational conversation

Abstract

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".

Processing inferences at the semantics/pragmatics frontier: Disjunctions and free choice

“…This cost has been used to argue against a default view of scalar implicature and, more generally, to answer questions about whether reasoning about alternatives should be understood as a late process or as an earlier pre-compiled operation. In the long run, these techniques may also be used to tease apart prominent approaches to scalar implicatures (e.g., Gricean, pragmatic approaches à la Spector, 2003, van Rooij & Schulz, 2004, Sauerland, 2004, Franke, 2011 and grammatical approaches à la Chierchia, 2004, Fox, 2007, Chierchia, Fox & Spector, 2008.…”

“…Recently, linguists showed that formal models used to derive scalar implicatures can be adapted to account for free choice inferences (inspired by Kratzer and Shimoyama, 2002, see Schultz, 2005, Klinedinst, 2006, Fox, 2007, Chemla 2008, 2010, Alonso-Ovalle, 2008, Franke, 2011. In most cases, the idea is to treat free choice inferences as second order scalar implicatures in the following sense.…”

Children's knowledge of free choice inferences

“…For the purposes of the example, we will adopt the theory proposed in Fox 2007, which argues that free choice inferences are a recursive type of scalar implicature. It should be understood that there are other scalar implicaturebased accounts, and some of them very different from Fox's theory, including accounts presented in Klinedinst 2007; Chemla 2010; van Rooij 2010;Franke 2011;Alonso Ovalle 2005;Chierchia 2013. Moreover, rather than going into Fox's theory in detail, we will simply sketch the intuition that underlies the theory.…”

Reply to commentaries

“…There is an important issue as to whether we should endorse shallow or rather deep reasoning models. Many game theoretic models that contain higher-order pragmatic reasoning of the kind envisaged by Jäkel and Liu exist (e.g., Franke 2011;Pavan 2013;Rothschild 2013;Jäger 2014), including models that consider probabilistic choice rules at each level of iteration (e.g., Bergen, Levy, and Goodman 2012;Franke and Jäger 2014;Bergen and Goodman 2015; Goodman to appear). The probabilistic speaker and listener rules given in our paper would map onto a level-1 speaker and a level-2 listener in so-called iterated best response models (Franke and Jäger 2014).…”