Information, Processes and Games (1604.02603v1)

Abstract: We survey the prospects for an Information Dynamics which can serve as the basis for a fundamental theory of information, incorporating qualitative and structural as well as quantitative aspects. We motivate our discussion with some basic conceptual puzzles: how can information increase in computation, and what is it that we are actually computing in general? Then we survey a number of the theories which have been developed within Computer Science, as partial exemplifications of the kind of fundamental theory which we seek: including Domain Theory, Dynamic Logic, and Process Algebra. We look at recent work showing new ways of combining quantitative and qualitative theories of information, as embodied respectively by Domain Theory and Shannon Information Theory. Then we look at Game Semantics and Geometry of Interaction, as examples of dynamic models of logic and computation in which information flow and interaction are made central and explicit. We conclude by looking briefly at some key issues for future progress.