Communicative Stability and the Typology of Logical Operators

The typology of the logical vocabulary in natural language is highly skewed. In the domain of logical connectives, AND and OR are often lexicalized, lexicalizations of NOR are less common and tend to be structurally complex, and no other logical connective is ever lexicalized. Existing accounts fail to fully derive this major crosslinguistic pattern, and moreover resort to otherwise unwarranted assumptions. The goal of this paper is to provide an account which is less stipulative and has wider empirical coverage than previous accounts, based on a novel notion of communicative stability. Using a model of a rational speaker we observe that attested languages are stable languages, i.e., languages in which the optimal message for a speaker to choose when they want to convey a particular state they are in is not affected by which states they take to be more likely and which ones less. We argue that Stability can account both for why AND and OR are the only simple connectives lexicalized and for why NOR is the only complex connective lexicalized.