Typical use of quantifiers: A probabilistic speaker model

Typical use of quantifiers: A probabilistic speaker model Michael Franke (m.franke@uva.nl) Institute for Logic, Language and Computation, University of Amsterdam Science Park, Kruislaan 107, 1098 XG Amsterdam, The Netherlands Abstract judgements are crucially different in kind from scalar impli- catures. This allows him to explain away experimental evi- dence that might otherwise speak for a grammatical view of scalar implicature (Chierchia, Fox, & Spector, 2012; Sauer- land, 2012). Obviously, then, understanding what typicality judgements are is also of theoretical significance. Taking sides with the integrated view informally ex- pounded by DT Goodman & Stuhlm¨uller, 2013). The formal ad- ditions are (i) the integration of a richer context model, bor- rowed from game theory, that allows for more flexibility in modeling the implicit question under discussion, i.e., what counts as relevant to a linguistic choice, and (ii) a gradient notion of salience of alternative expressions. The latter ex- tension is the most important one: whereas previous models of pragmatic reasoning look at a single fixed set of alternative expressions that compete in production, the present model al- lows for weaker or stronger activation of different alternatives and shows one possibility of integrating such a gradient no- tion of alternativeness in a comprehensive production model. More concretely, the model formalizes and tests the idea that typicality ratings reflect pragmatic appropriateness, in particular subjects’ considerations as to whether the quanti- fier some is a good lexical choice in a description of the pre- sented situation. To determine whether a description is prag- matically well-chosen, a comparison with alternative choices is needed. I submit that subjects assess various alternatives to some with a variable latent probability that will be estimated from the observed data. Pragmatic appropriateness of an en- tertained alternative is determined based on its interpretation by an imagined listener. This presupposes an implicit goal, and so I suggest that subjects rate a quantified sentence “Q of the As are Bs” based on how good an answer this is to the question under discussion “How many As are Bs? ” The paper is structured as follows. The next section intro- duces the relevant experimental approaches to typicality of some. After that, I introduce the Bayesian speaker model by first motivating a parameterized representation of the ques- tion under discussion and then spelling out the probabilis- tic production model on top of it. Subsequently, I show that the model yields a satisfactory explanation of the data from DT Gricean reason- ing; Bayesian cognitive modeling; game theory; alternatives Introduction Classically, the meaning of quantifiers is described in terms of clearcut binary truth conditions (e.g. Barwise & Cooper, 1981; Peters & Westerst˚ahl, 2006). For example, the sentence schema “Some of the As are Bs” is true just in case there is at least one A that is also a B. On top of that, it is widely held that the scalar quantifier some, if used in the appropriate contexts, conveys a scalar implicature, roughly, that some but not all of the As are Bs (c.f. Grice, 1975; Levinson, 1983). Again, this is usually treated as a categorical affair: in a given context an utterance either does or does not have an implicature. This beautiful picture, alas, appears to be too coarse- grained. A large body of psychological literature has demon- strated that subjects’ use and interpretation of quantifiers is strikingly regular but also rather fuzzy in manifold ways (c.f. H¨ormann, 1983; Moxey & Sanford, 1993). Two recent stud- ies by Degen and Tanenhaus (2011, to appear) and van Tiel (2014, to appear) showed that judgements of acceptability of sentences like “Some of the As are Bs” vary systematically but smoothly with the size of the set of As that are Bs (hence- forth: the target set). Whereas these sentence are atypical descriptions when the target set size is small or when it ap- proaches its maximum (i.e., the total number of As), this is not expected under the standard categorical picture (see Figure 1 and the following section for more on typicality judgements). It is controversial what empirically measured typicality judgements reflect. Degen and Tanenhaus (D&T) view the attested gradient patterns as evidence for a probabilistic ac- count of pragmatic interpretation. According to their favored constraint-based approach, multiple factors contribute to the probability with which a listener will draw a pragmatic infer- ence. From this point of view, gradient typicality judgements result from a fuzzy pragmatic interpretation process, of which scalar implicature calculation is a part. Unfortunately, D&T do not offer a concrete model with which to corroborate this position. In contrast, van Tiel (vT) maintains that typicality