A coalgebraic higher-order modal fixed-point logic

2026-07-21

AI Summary

This work proposes a higher-order modal fixpoint logic grounded in coalgebraic semantics to uniformly model and verify both nondeterministic and probabilistic systems. For the first time, it integrates coalgebraic methods into a higher-order modal fixpoint framework, establishing a formal semantic foundation for hybrid computational systems. Building on this logic, the authors reduce two classical decision problems—the emptiness problem for nondeterministic finite automata and the value-1 problem for probabilistic automata—to instances of model checking in the proposed logic. This reduction not only resolves these long-standing verification challenges but also demonstrates the logic’s expressive power and practical utility in automata theory and system verification.

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.

Problem

• coalgebraic logic
• higher-order modal fixed-point logic
• probabilistic automata
• non-deterministic finite automata
• model checking

Innovation

• coalgebraic logic
• higher-order modal fixed-point logic
• probabilistic automata
• model checking
• automata emptiness