A Panorama of Iterated Revision

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David Makinson on Classical Methods for Non-Classical Problems, 2014, 2014, pp. 71 - 94
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Almost three decades ago, DavidMakinson, together with Carlos Alchourron and Peter G¨ardenfors published their classical work on the logic of theory change, the renowned “AGM paper” [1]. From this paper the area of Belief Revision was born and hundreds of future publications drew inspiration from it and contributed to the development of the field. Yet in this survey we will not focus on what the AGM did do, but rather on what it left out: iterated belief revision. Let us set the stage with an example. Vasiliki is an archeologist participating in an excavation of an ancient temple near Athens. One day her trowel hits on an ancient Greek vase. The vase is a typical 3rd century BC Greek vase. The design, the painting, the archeological layer it was discovered in, all confirm without doubt that the vase was made in Greece some 2300 years ago. The big surprise however came when Vasiliki looked inside the vase. A small stone tablet with Maya script inscribed on it was lying inside! The discoverywasmind-blowing. To the young enthusiastic archeologist, eager to make a name for herself, this was without doubt concrete proof that Columbus was not the first European to reach America. The ancient Greeks had beat him by 1800 years! History books had to be rewritten! Vasiliki spent the night thinking of all the changes that had to be made in our theories about ancient Greeks (and perhaps ancient Mayas). The theory developed by Alchourron, G¨ardenfors, and Makinson, was designed to address precisely these kind of scenarios. A rational agent receives new reliable information ' that (in principle) contradicts her initial belief set K; the agent is thus forced to move to a new belief set K ˚ ' containing '. Moreover, the new belief set K ˚ ' has to be a rational change to K given '. The inner workings of the transition from K to K ˚ ' are studied and formalized in the AGM paper, setting the stage for a plethora of exciting results to follow over the next three decades.
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