Some formal results on the upward-monotonic bias, communicative stability, the strongest answer condition, and exhaustification

This paper extends a proposal by Bar-Lev and Katzir that stability, a property of alternative sets whereby the behavior of pragmatic speakers is not predicted to depend on the probabilistic prior, can help explain the prevalence of upward-monotonic operators in natural language. It is shown that stability can be given a non-probabilistic characterization as a strongest answer condition and related to the output of exhaustification operators, providing additional motivation for its desirability. Furthermore, stability constraints predict the preference for lexicalizing upward-monotonic logical functions.