Games, boards and play A logical perspective

Games are good models for analyzing crucial notions in logical reasoning and computation. This dissertation specifically delves into game graphs, game board change, and the logical analysis of game elements across various scenarios.
First, we analyze two sorts of games. The first kind of games we consider are sabotage games. We provide a complete axiomatization for the validities in the language of sabotage modal logic slightly extended with just enough expressive devices from hybrid logic.
Our next kind of game, i.e., the distributed game, concerns the difference between players’ internal view and the modeler’s external view of the game as it proceeds. In Chapter 4, we study these ‘distributed games’ with special logical languages allowing us to describe local and global perspectives.
The remaining topics of the thesis explore two further directions.
First, in Chapter 5 we note that the sabotage model logics in our first part can be seen as instances of a much broader class of logics with modalities describing various model changes. We explore what is the precise complexity of testing for the appropriate notions of bisimulation between given finite models.
Our final topic concerns another extension of distributed games for game scenarios, namely, in the functioning of global recommender systems interacting with local individual users. In Chapter 6 we show how the filtration dynamics can be specified and analyzed completely in dynamic-epistemic logics of communication involving filtering actions.
Finally, we highlight some unresolved issues for further exploration based on existing research.