Only, or, and free choice presuppositions.

Bar-Lev and Fox (Natl Lang Semant 28:175–223, 2020), B-L&F, redefine the exhaustification operator, Exh, so that it negates innocently excludable (IE) alternatives and asserts innocently includable (II) ones. They similarly redefine the exclusive particle only so that it negates IE-alternatives and presupposes II ones. B-L&F justify their revision of only on the basis of Alxatib's finding (in: Proceedings of NELS 44, 2014) that only presupposes free choice (FC) in cases like Kim was only allowed to eat soup or salad. I show challenges to B-L&F's view of only and argue against extending II to its meaning. Instead I propose that FC is better treated as a "presuppositional implicature" in such cases. I show the details of how this can be done and identify the necessary (and occasionally novel) auxiliary assumptions. [ABSTRACT FROM AUTHOR]