A coalgebraic higher-order modal fixed-point logic

Ryan Tay; Harsh Beohar; Charles Grellois

A coalgebraic higher-order modal fixed-point logic

Logic in Computer Science 2026-07-21 v1

Authors: Ryan Tay , Harsh Beohar , Charles Grellois

Abstract

We introduce a coalgebraic extension of the higher-order modal fixed-point logic (HFL) which subsumes both HFL and its probabilistic extension. We show that the emptiness problem for non-deterministic finite automata as well as the value-1 problem for probabilistic automata reduce to model-checking problems for this coalgebraic formulation of HFL.

Cite

@article{arxiv.2607.19160,
  title  = {A coalgebraic higher-order modal fixed-point logic},
  author = {Ryan Tay and Harsh Beohar and Charles Grellois},
  journal= {arXiv preprint arXiv:2607.19160},
  year   = {2026}
}

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17 pages