27 June 2023, NihiL Seminar, Aleksi Anttila & Søren Knudstorp

Abstract:

Within team semantics, a focal point of study has been that of expressive power (what properties can a given logic express). One such team logic is BSML, a modal team logic designed for modeling free choice inferences and related linguistic phenomena.

In recent work, Aloni et al. (2023) present two extensions of BSML, demonstrating their expressive completeness for all properties [invariant under bounded bisimulation] and all union-closed properties, respectively, and leave open the problem of characterizing the expressive power of BSML. Continuing this line of work, we solve this problem by showing that BSML is expressively complete for all convex, union-closed properties. This leads us to ponder a logic that is expressively complete for all convex properties simpliciter. We introduce a logic which accomplishes precisely that.