In this paper we introduce a cut-free sequent calculus for the alternation-free fragment of the modal $\mu$-calculus. This system allows for cyclic proofs and uses a simple focus mechanism to control the unravelling of fixpoints along infinite branches. We show that the proof system is sound and complete and apply it to prove that the alternation-free fragment has the Craig interpolation property.

翻译：在本文中,我们引入了一种无断裂的序列计算法,用于无变换模式元元计算法的零星碎片。 这个系统允许使用循环校准, 并使用一个简单的焦点机制来控制无穷树枝的固定点的解裂。 我们显示, 验证系统是健全和完整的, 并应用它来证明无变换模式的碎片具有克雷格内插特性 。