10 problems

Extension conjecture. Many of the complexity results proved for ${{\mathrm{PL}}\xspace(\normalfont\textsc{ne})}\xspace$ should extend naturally to other convex union-closed logics,…

Let $X$ be a team, let $\Sigma$ be a set of $k$-anonymity atoms, and let $\Sigma\vdash x\mkern 2mu\bm{\Upsilon}\mkern -3mu_{k}\mkern 2mu y$ denote derivability from $\Sigma$ using…

Non-necessity conjecture. Distributivity is not a necessary condition for validating the Split axiom even over finite classical frames; equivalently, there should be a finite class…

Let $\mathbf D(R)$ be a strongly first order dependency. A dependency is non-jumping when it has the non-jumping property considered in the paper. Decomposition conjecture. Every s…

Let $\mathbf D$ be a generalized dependency. It is relativizable if every sentence of $\texttt{FO}(\mathbf D^{(P)})$ is equivalent to some sentence of $\texttt{FO}(\mathbf D)$. Rel…

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 $\mathcal D^\uparrow$…

Team semantics evaluates formulas on teams, where a team is a set of assignments, and Mostowski quantifiers are interpreted using collections of subsets of the domain. Consideratio…

Let $\mathcal{L}$ be the logic discussed in the paper, and let $k\in\mathbb{N}$. Consider extensions of $\mathcal{L}$ obtained by attaching suitable operators of this type to its a…

Relationship conjecture. A close relationship exists between Paraconsistent Non-dependence Logic and Jaśkowski's Discussive Logic.