The languages of logics based on team semantics typically only allow atomic negation or restricted negation. In this paper, we explore propositional team-based logics with full (intuitionistic) negation. We demonstrate that including full intutionistic negation does not complicate the axiomatization of propositional team-based logics with the downward closure property. We also review known expressive completeness results for these logics, highlighting how relevant complemented properties are expressed in propositional dependence logic without directly using negation. Building on these insights, we also prove a new result: propositional logic extended with both dependence and inclusion atoms is expressively complete.

翻译：基于团队语义的逻辑语言通常仅允许原子否定或受限否定。本文探讨了具有完全（直觉主义）否定的命题团队逻辑。我们证明，引入完全直觉主义否定并不会使具有向下封闭性质的命题团队逻辑的公理化复杂化。同时，我们回顾了这些逻辑已知的表达完备性结果，重点说明了相关互补性质如何在命题依赖逻辑中无需直接使用否定即可表达。基于这些发现，我们还证明了一个新结果：同时扩展依赖原子与包含原子的命题逻辑具有表达完备性。