We initiate the study of the complexity-theoretic properties of convex logics in team semantics. We focus on the extension of classical propositional logic with the nonemptiness atom NE, a logic known to be both convex and union closed. We show that the satisfiability problem for this logic is NP-complete, that its validity problem is coNP-complete, and that its model-checking problem is in P.

翻译：我们首次系统研究了团队语义中凸逻辑的复杂性理论性质。重点关注经典命题逻辑通过非空原子NE的扩展——该逻辑已知同时具有凸性与并封闭性。我们证明该逻辑的可满足性问题是NP完全的，其有效性问题是coNP完全的，而其模型检测问题属于P类。