A Categorical Approach to Coalgebraic Fixpoint Logic

CoRR(2024)

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Abstract
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 μ-calculus in this framework, as well as PDL and a logic with a probabilistic dynamic modality.
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