Linguistic Variability and Adaptation in Quantifier Meanings

Linguistic Variability and Adaptation in Quantifier Meanings Ilker Yildirim, Judith Degen, Michael K. Tanenhaus, T. Florian Jaeger Department of Brain & Cognitive Sciences, University of Rochester, Rochester, NY 14627 {iyildirim, jdegen, mtan, fjaeger}@bcs.rochester.edu Abstract People’s representations of most and arguably all linguistic and non-linguistic categories are probabilistic. However, in lin- guistic theory, quantifier meanings have traditionally been de- fined set-theoretically in terms of categorical evaluation func- tions. In 4 “adaptation” experiments, we provide evidence for the alternative hypothesis that quantifiers are represented as probability distributions over scales (e.g., Zadeh, 1965). We manipulate exposure to different distributions of “some” and “many” and find that listeners adapt to those distributions, as predicted. Our results suggest that the interpretation of quanti- fiers is best modeled as a process involving rich, probabilistic representations. Keywords: Quantifiers; Semantics; Language processing; Adaptation; Generalization Figure 1: Illustration of across speakers variability in mean- ings of quantifiers. Introduction In linguistic theory, quantifier meanings have traditionally been defined set-theoretically in terms of categorical evalua- tion functions (Barwise & Cooper, 1981) yielding either truth or falsity of a sentence containing a quantifier. Quantifiers are understood as relations between sets: some(A, B) is true iff ||A|| ∩ ||B|| = many(A, B) is true iff ||A|| ∩ ||B|| > n, where n is some large number For example, the sentence Some candies are green is true just in case the intersection of the candies and the green things is not empty. Similarly, Many candies are green is true just in case the cardinality of the intersection of the candies and the green things is larger than some contextual norm n. This points to a notable feature of some quantifiers: they exhibit both vagueness and context-dependence (Solt, 2009). A class of alternative views tries to incorporate this feature by representing quantifiers probabilistically. For example, fuzzy logic (Zadeh, 1965) approaches to meaning consider quantifiers such as “some” as probability distributions over scales (e.g., Moxey & Sanford, 1993). Probabilistic quanti- fier semantics are at the heart of recent models of both syl- logistic reasoning (Chater & Oaksford, 1999) and scalar im- plicature (Goodman & Stuhlm¨uller, 2013). Here we provide further evidence that quantifiers are indeed interpreted in a probabilistic, graded manner. The novel empirical contribu- tion lies in addressing the adaptability of these distributions to variable language environments. The probabilistic view on quantifier meaning is illustrated in Figure 1a: “some” and “many” form graded distribu- tions over a contextually determined scale. 1 Previous work 1 For example, it is not as plausible to quantify 18 out of 1000 as “many” as to quantify 18 out of 20. has implicitly assumed that these distributions are invariant across linguistic environments, in that the distribution corre- sponding to, for example, “some” is stationary across differ- ent dialects, speakers, genres, and so on. However, variability in language use is the norm. Speak- ers differ in their realization of phonemes (cf. Allen, Miller, & DeSteno, 2003), lexical preferences (e.g., couch vs. sofa), as well as syntactic preferences (e.g., some speakers use pas- sives more often than others, Weiner & Labov, 1983). Such linguistic variability is a challenge for comprehenders that must be overcome to achieve successful communication. One solution for dealing with variable linguistic environments is to track and adapt to the joint statistics of linguistic categories (e.g. phonemes, words, syntactic structures) and contextual cues, including the speaker. A powerful way to test whether listeners adapt to the statis- tics of the input is to determine whether categorization func- tions shift with exposure. If listeners adapt to new environ- ments in which the statistics diverge from their prior beliefs, this would suggest that linguistic representations are sensi- tive to and adapt to such sources of variability. This reason- ing has been successfully applied to phonetic categories (e.g., Clayards, Tanenhaus, Aslin, & Jacobs, 2008; Vroomen, Lin- den, Gelder, & Bertelson, 2007; Kraljic & Samuel, 2006), prosodic categories (Kurumada, Brown, & Tanenhaus, 2012), and syntactic categories (Fine, Jaeger, Farmer, & Qian, under- review; Kamide, 2012). Here we ask whether listeners’ representations of the quan- tifiers “some” and “many” are probabilistic and sensitive to environmental variability. Figure 1b depicts hypothetical some and many distributions over cardinalities for two speak- ers whose use of the quantifiers differs. In four adaptation experiments, we provide evidence that quantifiers are represented as probability distributions. More-