Completeness and logical full abstraction in modal logics for typed mobile processes

We study an extension of Hennessy-Milner logic for the pi-calculus which gives a sound and complete characterisation of representative behavioural preorders and equivalences over typed processes. New connectives are introduced representing actual and hypothetical typed parallel composition and hiding. We study three compositional proof systems, characterising the May/Must testing preorders and bisimilarity. The proof systems are uniformly applicable to different type disciplines. Logical axioms distill proof rules for parallel composition studied by Amadio and Dam. We demonstrate the expressiveness of our logic through verification of state transfer in multiparty interactions and fully abstract embeddings of program logics for higher-order functions.