Modal Logics for Typed Mobile Processes

We propose an extension of Hennessy-Milner logic for the π-calculus which gives sound and complete characterisation of representative behavioural preorder and equivalence over typed processes. New connectives are introduced representing actual and hypothetical typed parallel composition and hiding. We study two compositional proof systems, characterising the May/Must testing preorders for infinite processes. The mixture of the two proof systems corresponds to bisimilarity. These proof systems are uniformly usable for different type disciplines. Logical axioms for composition originate from the corresponding proof rules studied by the preceding researchers including Amadio and Dam, allowing elimination of new connectives depending on types. We demonstrate how the use of types facilitates high-level logical reasoning through examples, including Milner’s encodings of data structures and business protocols.

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