Project Report KNOWLEDGE IN DIFFERENT SYSTEMS OF MODAL LOGIC 15-816 Modal Logic
نویسنده
چکیده
Modal logic is used by game theorists in the form of epistemic modal logic, where the operator is interpreted as a knowledge operator. This is useful because it allows the knowledge of players in games to be formalized and included in models of games. Then outcomes can be characterized by this knowledge, leading to theorems of the form “in games of type x, if all players have knowledge y, then solution z will be realized.” The system of modal logic used in this context is classical S5, a very strong system which translates into an epistemic logic with a very strong knowledge operator which may not be appropriate for all situations. The purpose of this project, therefore, is to examine the results of using other systems of modal logic, S4 and T, as a basis for the epistemic logic used by game theorists. A natural starting place for inquiry is Aumann’s framework and his well-known result that common knowledge of rationality implies the backward inductive outcome in perfect information games. It is shown in this paper that Aumann’s result does not depend on an S5-based framework; his result holds for S4and T-based frameworks as well.
منابع مشابه
Project Report Logic Programming in Constructive Provability Logic 15-816 Modal Logic
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