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The study of words that express quantification (e.g., some, most) has occupied philosophers, linguists, logicians, and psychologists since the work of Aristotle. The current consensus in formal semantics is that many or most quantifying expressions denote generalised quantifiers, i.e., relations between sets, with clearly defined but usually logically weak meanings. Evidence from psychological experiments on quantifier use and interpretation, however, suggests a rather different picture. For example, participants in experiments would infer from Some A are B that about a quarter of the A are B, rather than at least one A, as the usual semantic denotation of 'some' implies. We call these narrow ranges observed in experimental data 'focal ranges'.

Moreover, a quantifier’s focal range, as attested by experimental data, is usually not precisely characterised but may have a vague and elusive circumference. Still, regularities in quantifier use and interpretation persist, and so the main goal of this project is to build a bridge between formal semantics and psychological data of quantifier use and interpretation.

Our approach is pragmatic. We conjecture that apparent discrepancies between linguistic theory and experimental data can be resolved by pragmatics and that we can use the study of quantifier use to understand general pragmatic principles. The relevant principles crucially include further relevant cognitive factors, such as imprecision and error in the perception and processing of quantity, uncertainty about an interlocutor’s lexicon, uncertainty about contextually relevant levels of required precision, and limits on the extent to which language users are able or willing to engage in theory of mind reasoning to converge on optimal language use. Since such a psychologically rich picture can grow unwieldy very soon, we will make use of data-driven probabilistic modelling, following recent game-theoretic and Bayesian approaches.

Empirically, this project sets out to systematically collect data from a uniform family of tasks gauging the production and interpretation of quantifying expressions. We are specifically interested in potential asymmetries between speaker production and listener comprehension, as well as in dynamic alignment processes in repeated speaker-listener interaction. Moreover, we will recruit not only neurotypical adults, but also neurotypical children and adults with autism spectrum disorder. Both of these latter groups are known to experience pragmatic deficits. By collecting data using uniform stimuli and task types in static or dynamic settings from these different populations, we will be able to test, using explicit probabilistic modeling, extant theoretical accounts of the pragmatic abilities of children and adults with autism spectrum disorder.