We define a framework for incorporating alternation-free fixpoint logics into the dual-adjunction setup for coalgebraic modal logics. We achieve this by using order-enriched categories. We give a least-solution semantics as well as an initial algebra semantics, and prove they are equivalent. We also show how to place the alternation-free coalgebraic $\mu$-calculus in this framework, as well as PDL and a logic with a probabilistic dynamic modality.

翻译：我们定义了一个框架，用于将无交错不动点逻辑融入到上代数模态逻辑的对偶伴随结构中。通过使用序丰富范畴实现了这一目标。我们给出了最小解语义和初始代数语义，并证明两者等价。同时展示了如何将无交错上代数μ演算、命题动态逻辑以及包含概率动态模态的邏輯系统纳入该框架。