Coalition Logic studies what coalitions can enforce. Recent work treats inability as simple non-ability: $\neg\Eff{C}\varphi$. This conflates two distinct configurations -- a coalition unable to force $\varphi$ may still force $\neg\varphi$, retaining adversarial control rather than genuine inability. We introduce \textbf{Full Inability} ($\FI$): the symmetric condition in which a coalition can enforce neither a proposition nor its negation. Combining coalitional effectivity with propositional negation yields a four-fold spectrum: \textbf{Full Control} ($\FC$), \textbf{Positive Determination} ($\PD$), \textbf{Adverse Determination} ($\AD$), and \textbf{Full Inability} ($\FI$). These categories partition a coalition's strategic status exhaustively and exclusively. We establish their algebraic and order-theoretic structure. Under $α$-duality, propositional negation and coalition complementation generate a Klein four-group symmetry. In playable models, the four power regions are order-convex in the powerset lattice, yielding interval-stable verification of inability. We axiomatize $\CLFI$, a definitional extension treating Full Inability as a primitive modality. Via elimination translation, we prove soundness, completeness, and conservativity over Coalition Logic. The extension preserves expressive power and complexity ($\PSPACE$-complete), but provides direct proof-theoretic access to symmetric inability, strategic dependence, propositional dummyhood, and containment verification.

翻译：联合体逻辑研究联合体能够强制执行什么。近期研究将无能力简单处理为无能力：$\neg\Eff{C}\varphi$。这混淆了两种不同的构型——一个无法强制$\varphi$的联合体可能仍然能强制$\neg\varphi$，保留了对抗性控制而非真正的无能。我们引入**完全无能**（$\FI$）：一种对称条件，即联合体既无法强制某个命题，也无法强制其否定。将联合体效能与命题否定相结合，产生了一个四重谱系：**完全控制**（$\FC$）、**正向决定**（$\PD$）、**反向决定**（$\AD$）和**完全无能**（$\FI$）。这些类别穷尽且互斥地划分了联合体的战略状态。我们确立了它们的代数结构和序理论结构。在$\alpha$对偶性下，命题否定与联合体互补生成一个克莱因四元群对称性。在可博弈模型中，四个权力区域在幂集格中是序凸的，从而产生无能验证的区间稳定性。我们公理化$\CLFI$，这是一种将完全无能作为原始模态的定义扩展。通过消去翻译，我们证明了其相对于联合体逻辑的可靠性、完全性和保守性。该扩展保持了表达能力和复杂性（$\PSPACE$完全），但为对称无能、战略依赖性、命题虚拟性与包含性验证提供了直接的证明论途径。