A. Darwiche and J. Pearl. On the logic of iterated revision. Artificial Intelligence, 89:1--29, 1997. 39  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a plausibility ordering between possible states of the world, or as a preference relation between information sources from which an agent can derive his beliefs. On a semantic level, epistemic states have been represented by a total pre order on interpretations of the underlying logical language [5]. This total pre order models the agent s preferences between several situations. This pre order has been encoded according to several ways, ordinals [16] 17] possibilities [7, polynomials [15] However, the agent has not always a total pre order between situations at his disposal, but is only ....

A. Darwiche and J. Pearl. On the logic of iterated revision. Artificial Intelligence, 89:1-29, 1997.

....But, although very elegant, AGM characterization do not capture adequately iterated belief revision. Thus, iterated belief revision has been bought into focus during the last ten years, and new additional postulates have been proposed in order to characterize iterated belief revision (see e.g. [6, 11, 13, 3]) In all these approaches an epistemic state is something more complex than a simple knowledge base, it not only has to represent the agent s current beliefs, but also the strategy the agent uses in order to modify his beliefs in presence of a new item of information. Yet al..l these approaches ....

....propositional logic and is a function from E into F . The elements of the set E will be called epistemic states. The elements of F will be called the observables and is the projection function; so if Phi 2 E, Phi) is the observable part of Phi. Notice that this idea was already implicit in [6, 11] where the projection function is called Bel. From now on the epistemic states will be denoted by upper case Greek letters. The i.e. the set of propositional variables will be finite symbol will denote the logical consequence relation. By W we denote the set of classical interpretations, and ....

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A. Darwiche and J. Pearl. On the logic of iterated revision. Artificial Intelligence, 89:1--29, 1997.

.... extrapolation operator satisfies Sigma l= ha b; a b; a bi (the change from a to :a between 2 and 3 being certain, the preferred trajectory is the one containing no other changes) Now, Lehmann s iterated revision, and also most iterated revision operators defined on epistemic states (e.g. [7] [2] give [a b; a; a] a. The reason for this difference is that iterated revision is concerned with pieces of information concerning a static world, therefore, once the new information :a has cancelled the preceding one, the reasons to believe in b have disappeared. This strong ....

A. Darwiche and J. Pearl. On the logic of iterated revision. Artificial Intelligence, 89:1--29, 1997.

....[4] with Belief Change Systems. Other approaches start with the AGM postulates and augment them in order to characterize iterated revision. Boutilier [2] opts for an absolute minimization strategy. Lehmann [6] considers the agent s epistemic state as a sequence of observations. Darwiche and Pearl [3] show that the AGM postulates are too weak and propose additional postulates which constrain the relationship between the total pre orders associated with two successive epistemic states. Intuitively, in terms of pre orders, the DP postulates preserve the relative ordering between the models of ....

....original AGM postulates. On contrast, R4. is a stronger version of original AGM postulate; it requires the epistemic states to be strongly equivalent in order to be equally revised. If the weak equivalence is used the postulate is not satisfied. It can be noticed that Darwiche and Pearl[3] also strengthen this postulate using the equality instead of the equivalence between epistemic states. According to the definition of the revision operator, the (R5) and (R6) original AGM postulates can merge into a unique one (R5. The following result can be established : Theorem 2 The ....

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A. Darwiche and J. Pearl. On the logic of iterated revision. Artificial Intelligence, 89:1--29, 1997.

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A. Darwiche and J. Pearl. On the logic of iterated revision. Artificial Intelligence, 89:1--29, 1997. 39

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A. Darwiche and J. Pearl. On the logic of iterated revision. Artificial Intelligence, 89:1--29, 1997.

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