Probabilistic pragmatics explains gradience and focality in natural language quantification

An influential view in philosophy and linguistics equates the meaning of a sentence to the conditions under which it is true. But it has been argued that this truth-conditional view is too rigid and that meaning is inherently gradient and revolves around prototypes. Neither of these abstract semantic theories makes direct predictions about quantitative aspects of language use. Hence, we compare these semantic theories empirically by applying probabilistic pragmatic models as a link function connecting linguistic meaning and language use. We consider the use of quantity words (e.g., "some," "all"), which are fundamental to human language and thought. Data from a large-scale production study suggest that quantity words are understood via prototypes. We formulate and compare computational models based on the two views on linguistic meaning. These models also take into account cognitive factors, such as salience and numerosity representation. Statistical and empirical model comparison show that the truth-conditional model explains the production data just as well as the prototype-based model, when the semantics are complemented by a pragmatic module that encodes probabilistic reasoning about the listener's uptake.