Modal Logic and the Approximation Induction Principle

We prove a compactness theorem in the context of Hennessy-Milner logic. It is used to derive a sufficient condition on modal characterizations for the Approximation Induction Principle to be sound modulo the corresponding process equivalence. We show that this condition is necessary when the equivalence in question is compositional with respect to the projection operators.

💡 Research Summary

The paper investigates the relationship between modal logics, specifically Hennessy‑Milner Logic (HML), and the Approximation Induction Principle (AIP) used in process algebra. It begins by extending the syntax of HML to include not only the standard modalities ⟨a⟩φ and