Joachim Parrow, Johannes Borgström, Lars-Henrik Eriksson, Ramūnas Forsberg Gutkovas, and Tjark Weber. Log. Methods Comput. Sci., 17(1), 2021.
We define a general notion of transition system where states and action labels can be from arbitrary nominal sets, actions may bind names, and state predicates from an arbitrary logic define properties of states. A Hennessy-Milner logic for these systems is introduced, and proved adequate and expressively complete for bisimulation equivalence. A main technical novelty is the use of finitely supported infinite conjunctions. We show how to treat different bisimulation variants such as early, late, open and weak in a systematic way, explore the folklore theorem that state predicates can be replaced by actions, and make substantial comparisons with related work. The main definitions and theorems have been formalised in Nominal Isabelle.
@article{parrow21modal,
author = {Joachim Parrow and Johannes Borgstr{\"{o}}m and Lars-Henrik Eriksson and Ram{\={u}}nas Forsberg Gutkovas and Tjark Weber},
title = {Modal Logics for Nominal Transition Systems},
journal = {Log. Methods Comput. Sci.},
volume = {17},
number = {1},
year = {2021},
url = {https://lmcs.episciences.org/7137}
}