Positivity, (anti-)exhaustivity and stability

Abstract

Why are AND and OR the only binary connectives which are lexicalized as simplex? In this paper we point out a special property they have: They are the only meaningful connectives which enable the innocent exclusion of alternatives that are logically independent from the connectives arguments. We further observe that, as a result, they are the only meaningful connectives that can block prior probabilities from leading to anti-exhaustive interpretations (Cremers et al. 2022). This property of AND and OR can explain their lexicalizability once combined with the notion of Stability from Bar-Lev & Katzir (2022), while the theory that emerges has advantages over the Stability-based account of the typology we proposed in Bar-Lev & Katzir (2022).