A Categorical Approach to Coalgebraic Fixpoint Logic
arxiv(2024)
摘要
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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