Interactions between logic and games are various, and both of them can be used for analyzing each other. Games on graphs can be considered for modeling reachability problems, search problems, dynamic networks and social networks among others, providing a testbed for various computational problems. The popular Cops and Robber game is a case in point in this area which has been studied extensively from the algorithmic perspective along with its many variants. In this talk, I will introduce some logical proposals matching the game from different levels: modeler’s perspective and players’ perspective. In particular, I will show how adding a constant for equality may lead a logic undecidable, and provide formal tools to capture how players can reason in the process of a game. Many of their logical properties will be discussed, including their axiomatization, expressiveness and computational complexity, which would also shed light on the study of existing problems in product logic.

The talk is based on my recent works with Qian Chen (Tsinghua University), Sujata Ghosh (Indian Statistical Institute), Fenrong Liu (Tsinghua University), Katsuhiko Sano (Hokkaido University) and Yaxin Tu (Tsinghua University).