Game designers grapple with an interestingly indirect problem: they directly manipulate games, but they wish to shape the space of play that those games afford. This phenomenon is particularly critical for games intending to make external impact (e.g., in educational games) where the impact for players happens primarily during interactive play, as opposed to passive perception. My research aims to accelerate the exploratory design process by applying the resources of artificial intelligence to insights from design studies. By capturing a designer’s working knowledge in a formal design space model, I uncover significant opportunities to mechanize the exploratory design process using automated reasoning tools. In this talk, I describe applications of answer set programming (ASP, a constraint logic programming paradigm) and related technologies (such as symbolic model checking) to modeling the design spaces. These design space models underlie several synthesis and analysis tools required by multiple ongoing, large-scale educational game development projects. This work sheds new light on the nature of design problems in interactive domains and suggests an impactful way of applying automation to overcome bottlenecks in the creative design process. I close with a roadmap of future work that will make design space modeling more usable, expressive, and in-tune with the needs of design practitioners.