Not nothing Nonemptiness in team semantics

This dissertation collects together five papers on the expressive power, axiomatization, and proof theory of propositional and modal logics with team semantics.
The first paper studies the properties of bilateral state-based modal logic (BSML). This logic extends classical modal logic with a nonemptiness atom NE which is true in a team if and only if the team is nonempty. We introduce two extensions of BSML, show that the extensions are expressively complete, and develop natural deduction axiomatizations for the three logics.
In the second paper, we prove expressive completeness results for convex propositional and modal team logics. We introduce multiple propositional/modal logics which are expressively complete for the class of all convex propositional/modal team properties. We also show that BSML is expressively complete for the class of all convex and union-closed modal team properties invariant under bounded bisimulation.
In the third paper, we study the dual or bilateral negation in team logics. We show variants, for propositional and modal team logics, of Burgess' result to the effect that the dual negation in independence-friendly logic and dependence logic exhibits an extreme degree of semantic indeterminacy.
In the fourth paper, we provide axiomatizations for modal inclusion logic and two expressively equivalent variants of modal inclusion logic.
In the fifth paper, we introduce a sequent calculus for the propositional team logic with both the split disjunction and the inquisitive disjunction. The sequent calculus consists of a G3-style system for classical propositional logic together with deep-inference rules for the inquisitive disjunction.