Semantics Column

I am delighted to be able to present this overview of game comonads by Samson Abramsky and Luca Reggio. Though this is presented in the semantics column, it is a bridge between the world of semantics with its focus on "structure" and the world of combinatorics and logic. Many game-based techniques have been developed to capture the expressive power of different fragments of logic, for example logics with numerical bounds on the number of quantifiers or alternations, modal logics of various kinds. These restrictions on the logics have combinatorial implications on the models such as restricting the tree width.