Modality, Bisimulation and Interpolation in Infinitary Logic

Rohit Parikh has been one of the pioneers at the interface of modal and dynamic logic. Bringing dynamic, process-oriented concerns into modal logic has been a major move, whose repercussions are still being felt today. In this contribution, I consider the bridge concept of bisimulation, which links modal logic with computational process theories. Our main results show how its model-theoretic invariance properties, first established within first-order model theory, may be lifted to infinitary logic, a natural generalized habitat for theories of programs and processes. The techniques used for this purpose also suggest some further proof-theoretic uses, going beyond purely modal languages. to appear in M. Fitting, R. Ramanujan, & K. Georgatos, eds. "Festschrift for Rohit Parikh's 60th Birthday" Annals of Pure and Applied Logic.