## Ki Yung Ahn ; Ross Horne ; Alwen Tiu - A Characterisation of Open Bisimilarity using an Intuitionistic Modal Logic

lmcs:4666 - Logical Methods in Computer Science, August 10, 2021, Volume 17, Issue 3 - https://doi.org/10.46298/lmcs-17(3:2)2021
A Characterisation of Open Bisimilarity using an Intuitionistic Modal Logic

Authors: Ki Yung Ahn ; Ross Horne ; Alwen Tiu

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.

Volume: Volume 17, Issue 3
Published on: August 10, 2021
Accepted on: March 10, 2021
Submitted on: July 5, 2018
Keywords: Computer Science - Logic in Computer Science,F.4.1