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 the difference in typical proportions associated with the two expressions can be explained by our account.

Given current data, only a few binary Boolean operators are expressed in lexically simple fashion in the world's languages: and, or, nor. These do not occur in every combination, for example, nor is not observed by itself. To explain these cross‐linguistic patterns, we propose an encoding of Boolean operators as update procedures to accept or reject information in a context. We define a measure of conceptual simplicity for such updates, on which attested operators are conceptually simpler than the remaining Booleans. Moreover, we show that language evolution selects for the attested lexical inventories by minimizing the complexity of using a lexical inventory compositionally to convey precise information.

Natural languages exhibit many semantic universals, that is, properties of meaning shared across all languages. In this paper, we develop an explanation of one very prominent semantic universal, the monotonicity universal. While the existing work has shown that quantifiers satisfying the monotonicity universal are easier to learn, we provide a more complete explanation by considering the emergence of quantifiers from the perspective of cultural evolution. In particular, we show that quantifiers satisfy the monotonicity universal evolve reliably in an iterated learning paradigm with neural networks as agents.

Natural languages exhibit many \emph{semantic universals}: properties of meaning shared across all languages. In this paper, we develop an explanation of one very prominent semantic universal: that all simple determiners denote monotone quantifiers. While existing work has shown that monotone quantifiers are easier to learn, we provide a complete explanation by considering the emergence of quantifiers from the perspective of cultural evolution. In particular, in an iterated learning paradigm, with neural networks as agents, monotone quantifiers regularly evolve.

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).