Games, Planning, Categorial Grammars, and Control of Discrete Event Systems

What single thing could link all of these topics together? In this talk I'll introduce "spatial logic" , a logic in which you can form the parallel composition of two formulas. This is an idea which goes at least back to 1958, with Lambek's categorial grammar. When you combine spatial logic with temporal logic, you get a specification language in which you can describe desired properties of a controlled system, where you have to build a controller to run in parallel with a given "plant" so that the combined controlled system has certain temporal properties. It turns out that you can automatically synthesize a control strategy for such a requirement, if one exists.