A coalgebraic higher-order modal fixed-point logic

Ryan Tay; Harsh Beohar; Charles Grellois

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arXiv · 2607.19160

A coalgebraic higher-order modal fixed-point logic

Ryan Tay·Harsh Beohar·Charles Grellois

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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.

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Ryan Tay, Harsh Beohar, Charles Grellois. 2026-07-21. A coalgebraic higher-order modal fixed-point logic. https://arxiv.org/abs/2607.19160

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