A Characterisation of Open Bisimilarity using an Intuitionistic Modal Logic

Abstract

Open bisimilarity is defined for open process terms in which free variables may appear. The insight is, in order to characterise open bisimilarity, we move to the setting of intuitionistic modal logics. The intuitionistic modal logic introduced, called $\mathcal{OM}$, is such that modalities are closed under substitutions, which induces a property known as intuitionistic hereditary. Intuitionistic hereditary reflects in logic the lazy instantiation of free variables performed when checking open bisimilarity. The soundness proof for open bisimilarity with respect to our intuitionistic modal logic is mechanised in Abella. The constructive content of the completeness proof provides an algorithm for generating distinguishing formulae, which we have implemented. We draw attention to the fact that there is a spectrum of bisimilarity congruences that can be characterised by intuitionistic modal logics.

Modal Intuitionistic Logics as Dialgebraic Logics

“…Finally, the theory would benefit from a high-level comparison of dialgebraic equivalence notions in the style of Staton [79]. It would furthermore be interesting to see how these interact with the notions of bisimulations for modal (bi-)intuitionistic logics given in [1,38,45].…”

“…We call β ′′ the adjoint buddy of β. 1 If both α and β ′′ are natural isos, then we can define a functor S :…”