English

A Categorical Approach to Coalgebraic Fixpoint Logic

Logic in Computer Science 2024-05-02 v1

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

Keywords

Cite

@article{arxiv.2405.00237,
  title  = {A Categorical Approach to Coalgebraic Fixpoint Logic},
  author = {Ezra Schoen and Clemens Kupke and Jurriaan Rot and Ruben Turkenburg},
  journal= {arXiv preprint arXiv:2405.00237},
  year   = {2024}
}
R2 v1 2026-06-28T16:12:19.878Z