MoL-2003-03: A Combined System for Update Logic and Belief Revision

MoL-2003-03: Aucher, Guillaume (2003) A Combined System for Update Logic and Belief Revision. [Report]

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Roughly speaking, in this thesis we will propose a logical system merging update logic as conceived by A.Baltag, L.Moss, S.Solecki on the one hand; and belief revision theory as conceived by C.Alchourron, P.Gardenfors and D.Mackinson (viewed from the point of view of W.Spohn) on the other hand. Before tackling the topic, we need to set out some general assumptions about the type of phenomenon that we intend to study thanks to these theories. It will also indirectly provide us a framework for our future work, and give an idea of the topic of this thesis (and these theories). We assume that any situation s involving several agents can be rendered from the point of view of the agents' knowledge and beliefs of the situation by a mathematical model M. We assume that this association is correct, in the sense that every intuitive judgement concerning s corresponds to a formal assertion concerning M. Now in the situation s, an action a may occur. We also assume that this action a can be correctly (see above) rendered from the point of view of the agents' knowledge and beliefs by a mathematical model \Sigma. Now in reality the agents update their knowledge and beliefs according to these two pieces of information: action a and situation s, giving rise to a new actual situation s x a. We assume again that we can render this update mechanism by a mathematical update (X) such that, as above, M (X) \Sigma corresponds correctly (see above) to s x a. Moreover we assume that the update mechanism concerning the agents' beliefs be the closest possible to a belief revision (conceived by AGM). Note that in reality, once the agents receive the new information carried by the action a, update their knowledge and beliefs. This double process may be done simultaneously in reality by the agents. Yet we carefully separate it in our approach by introducing \Sigma because these are two conceptually different things: apprehension of the new information (corresponding to \Sigma and update (corresponding to the update (X), on the basis of this apprehension. By the very nature of the BMS and AGM theories, merging them seems one of the best ways to give concrete form to these assumptions. Yet the resulting system should be a genuine logical system and we must keep that in mind. So, first we will set out these theories. Second, we will propose a merge system of these theories. Third we will propose a proof system for this system (with the introduction of a special canonical model in the completeness proof). Finally, we will compare our system with other similar systems, and also the AGM theory.

Item Type: Report
Report Nr: MoL-2003-03
Series Name: Master of Logic Thesis (MoL) Series
Year: 2003
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38

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