A Categorical Approach to Coalgebraic Fixpoint Logic
<|reference_start|>A Categorical Approach to Coalgebraic Fixpoint Logic: 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.<|reference_end|>
@article{schoen2024a,
    title={A Categorical Approach to Coalgebraic Fixpoint Logic},
    author={Ezra Schoen, Clemens Kupke, Jurriaan Rot, and Ruben Turkenburg},
    journal={arXiv preprint arXiv:2405.00237},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.00237},
    primaryClass={cs.LO}
}