Logic in Play

Going beyond the traditional focus on consequence and inference, logic can be broadened to an exact theory of general information-driven agency drawing on many sources, without giving up on its well-established mathematical modus operandi. We show how this broader agenda involves the design of new kinds of dynamic logics for action, information, knowledge update, and belief change, and eventually, entangled with these, agents’ preferences and goals. In particular, we explore several active interfaces of logic and games, where all these themes come together in natural concrete scenarios, ending up with advocating a move from game theory to a theory of play. Our presentation throughout takes the form of discussing typical examples, identifying major themes and suggesting new open problems concerning logic and agency. Finally, we explore what taking this agency-based perspective means for a variety of fields, including philosophy, linguistics, and game theory—and we conclude with some thoughts on what the field of logic is, or can become, in the perspective presented in this article