A Characterisation of Open Bisimulation using an Intuitionistic Modal Logic

Open bisimulation is the greatest bisimulation congruence for the π-calculus. In open bisimulation, free names in processes are treated as variables that may be instantiated; in contrast to late bisimulation where free names are constants. An established modal logic due to Milner, Parrow, and Walker characterises late bisimulation, that is, two processes satisfy the same set of formulae if and only if they are bisimilar. We propose an intuitionistic variation of this modal logic and prove that it characterises open bisimulation. The soundness proof is mechanised in Abella. The completeness proof provides an algorithm for generating distinguishing formulae, which can be used to explain and certify whenever processes are non-bisimilar.