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arXiv · 2405.00237

A Categorical Approach to Coalgebraic Fixpoint Logic

Ezra Schoen·Clemens Kupke·Jurriaan Rot·Ruben Turkenburg
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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 $\mu$-calculus in this framework, as well as PDL and a logic with a probabilistic dynamic modality.

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Ezra Schoen, Clemens Kupke, Jurriaan Rot, Ruben Turkenburg. 2024-04-30. A Categorical Approach to Coalgebraic Fixpoint Logic. https://arxiv.org/abs/2405.00237

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