Decisions, Actions, and Games: A Logical Perspective

Over the past decades, logicians interested in rational agency and intelligent interaction studied major components of these phenomena, such as knowledge, belief, and preference. In recent years, standard `static' logics describing information states of agents have been generalized to dynamic logics describing actions and events that produce information, revise beliefs, or change preferences, as explicit parts of the logical system. [22], [1], [12] are up-to-date accounts of this dynamic trend (the present paper follows Chapter 9 of the latter book). But in reality, concrete rational agency contains all these dynamic processes entangled. A concrete setting for this entanglement are games --- and this paper is a survey of their interfaces with logic, both static and dynamic. Games are intriguing also since their analysis brings together two major streams, or tribal communities: `hard' mathematical logics of computation, and `soft' philosophical logics of propositional attitudes. Of course, this hard/soft distinction is spurious, and there is no natural border line between the two sources: it is their congenial mixture that makes current theories of agency so lively.

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