Special Session on Logic and Games

Time: Nov 26, 2022

Venue: Zoom Online

Chair: Fenrong Liu

13:30-14:15 Jeremy Seligman (Auckland University): Mohist logic of Sudoko

14:15-14:40 Penghao Du (Tsinghua): Bisimulation and Axiomatization of Definable Link Cutting Logic

14:40-15:00 Break Time

Chair: Chenwei Shi

15:00-15:25 Qian Chen (Tsinghua): More on Hide and Seek Logic

15:25-16:05 Dazhu Li (Chinese Academy of Sciences): How do Players Reason in Cops and Robber Game?

16:05-16:50 Katsuhiko Sano (Hokkaido University): Axiomatizing a Simple Logic of the Hide and Seek Game

Concluding remarks: Johan van Benthem (Tsinghua and Stanford)

Closing words

SPECIAL SESSION “LOGIC AND GAMES”, Tsinghua University Closing words 26 November 2022

Johan van Benthem

This has been a small expert meeting on a highly technical subject that may look quite intimidating to outsiders. But at the same time, it was a meeting of a close circle of friends from China, India, Japan, New Zealand and The Netherlands.

Graph games are an attractive concrete model for studying large issues like strategic behavior or, in our more recent variants, the role of knowledge and ignorance in games. These games model a variety of real-world scenarios, but at the same time, they raise a surprising amount of subtle logical issues, witness the talks we heard from Penghao Du, Qian Chen, Dazhu Li and Katsuhiko Sano, especially on the Hide and Seek logic develo- ped by the Tsinghua group in close collaboration with Sujata Ghosh and her coworkers. Many new technical questions came up today, which we can keep discussing for a long time. Yet Jeremy also encouraged us to keep thinking about the larger issues at stake in our projects, and which essential features make our new kinds of game logics special. One sort of broader perspective already came up in several talks that we heard, namely, new conceptual connections with other fields, such as modal logics of dependence, hybrid logics, and the theory of ‘system combination’ in modal product logics. Finally, Jeremy’s talk on Mohist Logic and Sudoku Puzzles opened the windows much more widely, and highlighted the many subtle issues of inference and introducing helpful new notions in logical reasoning in games that go beyond current semantic frameworks. Perhaps the Mohist ancestors of our Chinese colleagues can still guide our path in identifying the basic relevant concepts here. Martin even reminded us of the possible moral dimension behind the original Mohist enterprise, by which time we are of course entering the wonderland of classical Chinese philosophy. I am sure that this historical and philosophical Sudoku theme, too, will reverberate in our minds long after today.

Finally, our meeting was on-line, unlike the gathering as originally planned. Indeed, we seem confronted with a new variety of sabotage games, with the Tsinghua campus map as the graph, a Demon (‘the system’) tries to prevent us Travelers from going where we want to be, with checkpoints and even occasional walls, and behind that, there is a third stochastic player, the behavior of the Corona Virus – a well-known modeling ploy from game theory or modern studies of causality. But studying this new probabilistic variant of the game would only offer the cool consolation of mathematics. Martin and I were told that coming to China right now just means a lot of on-line meetings here which we could just as well have done in the comfort of our homes in Holland. But to me personally, there is a difference. Here in Beijing there is that bleak reality, but also the hope of meeting the Chinese colleagues and students so close by. It is that hope which gives this workshop its special flavor, and I thank the organizers for making it happen.