The so-called "free choice" inference (from "You may take an apple or a pear" to "You may take an apple") is mysterious because it does not follow from ordinary modal logic. We show that this inference arises in the Rational Speech Acts model (Frank and Goodman, 2012). Our basic idea is inspired by exhaustification-based models of free choice (Kratzer and Shimoyama 2002, Fox 2007) and by game-theoretic accounts based on iterated best response (Franke, 2011). Specifically, we assume that when the speaker utters "You may take an apple or a pear", the hearer reasons about why the speaker did not choose alternative utterances such as "You may take an apple". A crucial ingredient in our explanation is the idea of lexical uncertainty (Bergen et al. 2016). Specifically, we assume that the speaker is uncertain whether or not the hearer will interpret "You may take an apple" as forbidding them from taking a pear; this is analogous to Fox's (2007) concept of optional recursive exhaustification. Uttering the disjunction is a way for the speaker to prevent the hearer from concluding about any fruit that it is forbidden to take it. Knowing this, the hearer concludes that there is no forbidden fruit.
Bergen, Leon, Roger Levy & Noah D. Goodman. 2016. Pragmatic reasoning through semantic inference. Semantics and Pragmatics 9(20). http://dx.doi.org/10.3765/sp.9.20.
Fox, Danny. 2007. Free choice and the theory of scalar implicatures. In Uli Sauerland & Penka Stateva (eds.), Presupposition and implicature in compositional semantics, 71–120. London, UK: Palgrave Macmillan. http://dx.doi.org/10.1057/9780230210752_4.
Frank, Michael C. & Noah D. Goodman. 2012. Predicting pragmatic reasoning in language games. Science 336(6084). 998–998. http://dx.doi.org/10.1126/science.1218633.
Franke, Michael. 2011. Quantity implicatures, exhaustive interpretation, and rational conversation. Semantics and Pragmatics 4(1). 1–82. http://dx.doi.org/10.3765/sp.4.1.
Kratzer, Angelika & Junko Shimoyama. 2002. Indeterminate pronouns: The view from Japanese. In Yukio Otsu (ed.), 3rd Tokyo conference on psycholinguistics, 1–25. http://dx.doi.org/10.1007/978-3-319- 10106-4_7.