Theoretical Aspects of Reasoning About Knowledge. by Ronald Fagin

By Ronald Fagin

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Cn> Our target is to construct a plausibility ordering over the possible failures of the circuit. A failure is taken to be a set of faulty components. We assume that failures of individual components are independent of one another. If we also assume that the probability of each component failing is the same, we can construct a plausibility ordering as follows: Let e be the probability that a single component fails. Then the probability of 4 We follow the standard notion for plausibility [Lew73, KLM90, Pea89], which uses the (perhaps confusing) convention of placing the more plausible event on the left of the -< operator.

Stalnaker, Knowledge, Belief, and Counter factual Reasoning in Games, forthcoming in the proceedings of the second Castiglioncello conference 1992, edited by C. Bicchieri and B. Skyrms. 43 A Knowledge-Based Framework for Belief Change Part I: Foundations Nir Friedman Stanford University Dept. edu Joseph Y. com Abstract We propose a general framework in which to study belief change. We begin by defining belief in terms of knowledge and plausibility: an agent believes φ if he knows that φ is true in all the worlds he considers most plausible.

Whatever arithmetic is necessary to describe the game and compute π*, along with a suitable coding of the game and associated payoffs. As before, we will leave this unspecified. Moreover, W will contain all formulas of the form (1) and (2). On the other hand, D will specify the set of paths to be used in inferring the players' behavior. This set of paths will vary according as the node that has been reached in the game lies on or off the equilibrium paths. Let a be the root, and T a propositional constant representing truth.

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