Heavy Tails and the Shape of Modified Numerals

The pattern of implicatures of the modified numeral “more than n” depends on the roundness of n. Cummins et al. (2012) present experimental evidence for the relation between roundness and implicature patterns and propose a pragmatic account of the phenomenon. More recently, Hesse and Benz (2020) present more extensive evidence showing that implicatures also depend on the magnitude of n and propose a novel explanation based on the approximate number system (Dehaene, 1999). Despite the wealth of experimental data, no formal account has yet been proposed to characterize the full posterior distribution over numbers of a listener after hearing “more than n.” We develop one such account within the Rational Speech Act framework, quantitatively reconstructing the pragmatic reasoning of a rational listener. We argue that world knowledge about the distribution of the true quantity has a substantial impact on the information conveyed by the modified numeral. We show that our pragmatic account in combination with a heavy-tailed model of the participants' prior correctly predicts various features of the experimental data from Hesse and Benz (2020)

An Alternatives Account of ‘Most’ and ‘More Than Half’

While ‘most’ and ‘more than half’ are generally assumed to be truth-conditionally equivalent, the former is usually interpreted as conveying greater proportions than the latter. Previous work has attempted to explain this difference in terms of pragmatic strengthening or variation in meanings. In this paper, we propose a novel explanation that keeps the truth-conditions equivalence. We argue that the difference in typical sets between the two expressions emerges as a result of two previously independently motivated mechanisms. First, the two expressions have different sets of pragmatic alternatives. Second, listeners tend to minimize the expected distance between their representation of the world and the speaker’s observation. We support this explanation with a computational model of usage in the Rational Speech Act framework. Moreover, we report the results of a quantifier production experiment. We find that our account can explain the difference in typical proportions associated with the two expressions

Neural Networks Track the Logical Complexity of Boolean Concepts

The language of thought hypothesis and connectionism provide two main accounts of category acquisition in the cognitive sciences. However, it is unclear to what extent their predictions agree. In this article, we tackle this problem by comparing the two accounts with respect to a common set of predictions about the effort required to acquire categories. We find that the two accounts produce similar predictions in the domain of Boolean categorization, however, with substantial variation depending on the operators in the language of thought