Explaining gaps in the logical lexicon of natural languages: A decision-theoretic perspective on the square of Aristotle

Across languages, certain logically natural concepts are not lexicalized, even though they can be expressed by complex expressions. This is for instance the case for the quantifier not all. In this paper, we propose an explanation for this fact based on the following idea: the logical lexicon of languages is partly shaped by a tradeoff between informativity and cost, and the inventory of logical expressions tends to maximize average informativity and minimize average cost. The account we propose is based on a decision-theoretic model of how speakers choose their messages in various situations (a version of the Rational Speech Act model). EARLY ACCESS