Explaining gaps in the logical lexicon of natural
languages
A decision-theoretic perspective on the square of
Aristotle
Émile Enguehard, Benjamin
Spector
Abstract
Across languages, certain
logically natural concepts are not lexicalized, even though theycan 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 betweeninformativity 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
speakerschoose their messages in various situations (a modified version of the Rational
Speech Act model).