5 problems

Characterization conjecture. A family of dependencies $\mathcal D$ is strongly first order if and only if every dependency $\mathbf D\in\mathcal D$ is strongly first order.

Let $\mathbf D(R)$ be a strongly first order dependency, and let global disjunctions be added to the language of team semantics alongside upwards closed dependencies and constancy…

Let $\mathbf D(R)$ be a strongly first order dependency, meaning that every sentence of $\texttt{FO}(\mathbf D)$ is equivalent to a first order sentence. Let $\mathcal D^\uparrow$…

Modal dependence logic and propositional independence logic are logics with disjunctive normal forms similar to those used for propositional logics of dependence. Conjecture. The a…

Open-formula correspondence conjecture. The open formulas of $\mathcal{D}({\sf M})$ correspond in an analogous manner to the downwards monotone properties of ${\rm CH}$.