BOUTILIER G., "Iterated Revision and Minimal Change of Conditional Beliefs", Journal of Philosophical Logic, vol. 25, 1996, p. 263--305.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....is believed in the belief set associated with the E relation i# it is true in all the most plausible worlds according to . 3 Revision of E relations In [Nay 94] Nayak deviates from the basic AGM framework in two ways. Firstly, in order to help us deal with iterated revision (see [Bou 96, DP 97, Wil 94] he argues that we need not only a description of the new belief set which results from a revision, but also a new E relation which can then guide any further revision. Thus we should enlarge our epistemic state to consist of a belief set together with an E relation and then ....

C. Boutilier, Iterated revision and minimal change of conditional beliefs, Journal of Philosophical Logic 25 (1996) 262--305.

....way to perform further revisions on the new knowledge base does not depend on the way the old knowledge base was revised. Numerous proposals have tried to state a logical characterization that adequately models iterated belief change behaviour [ Darwiche and Pearl, 1997; Darwiche and Pearl, 1994; Boutilier, 1996; Lehmann, 1995; Nayak et al. 1996; Nayak, 1994; Konieczny and Pino P erez, 2000 ] The more famous one seems to be [ Darwiche and Pearl, 1997 ] The main idea that is common to all of these works is that the belief base framework is not sucient to encompass iterated revision, since one ....

....accepted. An epistemic state allows to code the agent s beliefs but also to code her relative con dence in alternative possible states of the world. Epistemic states can be represented by several means: pre orders on interpretations [ Darwiche and Pearl, 1997; Lehmann, 1995 ] conditionals [ Boutilier, 1996; Darwiche and Pearl, 1997 ] epistemic entrenchments [ Williams, 1994; Nayak, 1994 ] prioritized belief bases [ Benferhat et al. 1999; Benferhat et al. 2000 ] etc. In this work we will focus on the representation of epistemic states in terms of pre orders on interpretations. In [ Konieczny ....

C. Boutilier. Iterated revision and minimal change of conditional beliefs. Journal of Philosophical Logic, 25(3):262-305, 1996.

....(C3) and (C4) In [DP97] Darwiche and Pearl have rephrased their postulates (and AGM ones) in terms of epistemic states instead of knowledge bases. In this way, they have removed these contradictions. 2. 3 Boutilier natural revision Before the work of Darwiche and Pearl, Boutilier proposed in [Bou93, Bou96] a natural revision operator which aims to have good iteration properties. This principle is called absolute minimization by Darwiche and Pearl and can be characterized by [Bou93] CB) If : then ( Which gives the following condition on the assignment: DP97] Theorem 3 ....

C. Boutilier. Iterated revision and minimal change of conditional beliefs. Journal of Philosophical Logic, 25(3):262-305, 1996.

....new evidence and the resulting knowledge base. But the way to perform further revisions on the new knowledge base does not depend on the way the old knowledge base was revised. Numerous proposals have tried to state a logical characterization that adequatly models iterated belief change behaviour [8, 7, 5, 13, 17, 16, 12]. The more famous one seems to be [8] The main idea that is common to all of those works is that the belief base framework is not sucient to encompass iterated revision, since one needs some additional information for coding the revision policy of the agent. So the need of epistemic states to ....

....to encode the agent state of mind is widely accepted. An epistemic state allows to code agent s beliefs but also to code its relative con dence in alternative possible states of the world. Epistemic states can be represented by several means: pre orders on interpretations [8, 13] conditionals [5, 8], epistemic entrenchments [21, 16] prioritized belief bases [2, 3] etc. In this paper we will focus on the representation of epistemic states in terms of pre orders on interpretations. What we propose in this paper is not yet an other logical characterization, but the de nition of a family of ....

C. Boutilier. Iterated revision and minimal change of conditional beliefs. Journal of Philosophical Logic, 25(3):262-305, 1996.

....starting from individual rules and individual facts. The result of the revision is itself in normal form, so that iterated revision is well defined, contrary to what results for standard AGM belief set revision. For ways of modifying the AGM theory in order to allow iterated revision, see:[2], 6] Minimax revision o#ers a clear definition of so called multiple revision, that is revision by means of a set of sentences. When contraction is considered as the main operation, using a set of sentences instead of one often results in unclear intuitions (see [5] Extensionality does not ....

Boutilier, C., Iterated Revision and Minimal Change of Conditional Beliefs. Journal of Philosophical Logic, 25, pp.263-305 (1996)

....information is available, contrary to what happens in the classical AGM approach, and it can be easily extended to manage them, when available. We use revision as the primitive operator, although it is often argued that contraction should be used as a primitive operator (see [8] see also [4] for a different view) however, it seems rather unnatural to suppose that our agents should change their minds about properties of the world were it not for the necessity of incorporating in their knowledge base a new fact. Exploration by means of sensors always yields new data to be added in ....

Boutilier, C.: (1996) Iterated Revision and Minimal Change of Conditional Beliefs, Journal of Philosophical Logic, 25: 263--305.

....starting from individual rules and individual facts. The result of the revision is itself in normal form, so that iterated revision is well defined, contrary to what results for standard AGM belief set revision. For ways of modifying the AGM theory in order to allow iterated revision, see:[2], 6] Minimax revision offers a clear definition of so called multiple revision, that is revision by means of a set of sentences. When contraction is considered as the main operation, using a set of sentences instead of one often results in unclear intuitions (see [5] Extensionality does not ....

Boutilier, C., Iterated Revision and Minimal Change of Conditional Beliefs. Journal of Philosophical Logic, 25, pp.263-305 (1996)

....it leaves some freedom in what the next sphere system S p should be. There are various proposals for rules for updating plausibility rankings, some of them with axiomatic characterizations (several are presented in Kelly s paper (Kelly 1988) such as (Darwiche and Pearle 1997) Nayak 1994) and (Boutilier 1996)) Once we have iterated belief change in view, it is natural to ask what the long run behaviour of methods for iterated belief change is. This is a familiar 30 Oliver Schulte question for Bayesians: results that show long run convergence to correct beliefs via conditioning have long since been ....

Boutilier, C. (1996). Iterated revision and minimal change of conditional beliefs. Journal of Philosophical Logic 25, 263-305.

....the object language to include counterfactual statements. Grahne [ 1991 ] points out that updating does not suffer from this problem. As such, it can be used to encode knowledge bases which include counterfactual axioms, or to evaluate embedded counterfactuals. An alternative approach is that of Boutilier [ 1995 ] who takes the AGM theory of revision together with the Ramsey test as a starting point, and extends the theory to support revision of conditional belief sets. Although he is able to avoid the problem of Gardenfors s triviality theorem, whether or not revision is an appropriate change operation ....

Boutilier, Craig 1995. Iterated revision and minimal change of conditional beliefs. Journal of Philosophical Logic To appear.

....(C3) and (C4) In [DP97] Darwiche and Pearl have rephrased their postulates (and AGM ones) in terms of epistemic states instead of knowledge bases. In this way, they have removed these contradictions. 2. 3 Boutilier natural revision Before the work of Darwiche and Pearl, Boutilier proposed in [Bou93, Bou96] a natural revision operator which aims to have good iteration properties. This principle is called absolute minimization by Darwiche and Pearl and can be characterized by [Bou93] CB) If : then ( That give the following condition on the assignment: DP97] Theorem 3 ....

C. Boutilier. Iterated revision and minimal change of conditional beliefs. Journal of Philosophical Logic, 25(3):262-305, 1996.

...., then KP 2Y[Z] badc P One of the major issues in this area is that of iterated belief change, i.e. modeling how the agent s beliefs change after multiple belief revisions or updates occur. Two of the main developments in this area are the work of Darwiche and Pearl [6] and Boutilier [4]. Darwiche Pearl put forward the following postulates as a way of extending the AGM revision postulates to handle iterated revision. 8 (DP1) If ITH , then = e=MI F=MI (DP2) If ITH , then K= U=MI F=MI (DP3) If =MI , then A = U=MI (DP4) If ) ....

....which uses a fixed plausibility ordering on situations and simply drops situations that conflict with sensing results from the , relation avoids both of these problems. Another interesting difference between our approach and many of the proposals for modifying the plausibility ordering [4, 6, 21, 22] is that they adopt orderings over possible worlds which do not contain a history of the actions that have taken place in the world. Our approach, on the other hand, is based on situations, which do have such histories. While Friedman and Halpern [8] do not adopt situations, their possible worlds ....

Craig Boutilier. Iterated revision and minimal change of conditional beliefs. Journal of Philosophical Logic, 25(3):262--305, 1996.

....case of belief revision (that is, revising previously revised beliefs) The AGM postulates restrict an agent s beliefs after a single revision, but provide no assistance in determining what an agent ought to believe after a sequence of revisions. Work on extending AGM to the iterated case includes [8, 11, 12, 19, 22, 26], but it is fair to say that as of now the theory of iterated belief revision is not a settled matter; see [13] for discussion of some of the outstanding issues. Our direct interest lies in multi agent belief revision, that is, the situation in which an agent is informed by multiple other agents, ....

....revision operators we consider here are, like fusion, history dependent. 12 As it so happens, not only does this invariance not hold for any of the proposals, but in each case it is possible to even get con icting results depending on the revision order. We consider here the proposals in [8, 11, 25, 19, 26]. We describe each of these proposals below and show that there exists at least one example such that (a) all ve proposals agree on the result of iterated revision, for any xed association order of revision, and (b) these di erent orders of revision yield belief sets that are not only distinct, ....

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Craig Boutilier. Iterated revision and minimal change of conditional beliefs. Journal of Philosophical Logic, 25:263-305, 1996.

....by conditionals in the AGM theory. A theorem is also presented in [BG93] which characterizes all of the unnested conditionals accepted after the revision M A B in terms of the conditionals in M . The acceptance of the Ramsey Test also allows for revision of right nested conditionals [Bou93, Bou96] Accepting a nested conditional A (B C) into a knowledge base K simply requires testing for acceptance of B C in K A , which will be true if C is accepted in (K A ) B . It is also shown in [Bou96] that for any revision sequence ( K A 1 ) A 2 : An there exists a ....

....of the Ramsey Test also allows for revision of right nested conditionals [Bou93, Bou96] Accepting a nested conditional A (B C) into a knowledge base K simply requires testing for acceptance of B C in K A , which will be true if C is accepted in (K A ) B . It is also shown in [Bou96] that for any revision sequence ( K A 1 ) A 2 : An there exists a sentence ff such that ( K A 1 ) A 2 : An = K ff and so any revision sequence can be stated in terms of a single revision by some sentence ff. Darwiche and Pearl also find fault with (K 4) DP97] ....

Craig Boutilier. Iterated revision and minimal change of conditional beliefs. Journal of Philosophic Logic, 25(3):262--305, 1996.

....shows that the conservative strategy can be captured in the context of basic belief change by a single additional axiom. Finally, we compare the present approach to existing work in the literature. It turns out that this form of conservative belief change has been characterized semantically by Boutilier (1993, 1996) in the context of the full AGM theory that presupposes dispositional coherence. Unfortunately, a decisive weakness of Boutilier s approach carries over to our more general context. We 5 In Rott (1998a) a fourth concept of coherence shows up: the temporal coherence of strategies to deal with ....

....In such a context of dynamic conjunction , #7) and (#8) would of course say something about diachronic coherence. The concept of conjunction that is being used in his paper, however, is the classical, symmetrical one. 26 See Rott (1996, Chapter 4) In this respect, I very much disagree with Boutilier (1996, p. 272) who finds these postulates quite mild. While it is true that AGM say next to nothing about the problem of iterated belief change, their conditions (#7) and (#8) as conditions constraining revisions by di#erent inputs, are very powerful indeed. They basically imply that all beliefs in ....

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Boutilier, Craig: 1996, `Iterated Revision and Minimal Change of Conditional Beliefs', Journal of Philosophical Logic 25, 263--305.

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BOUTILIER G., "Iterated Revision and Minimal Change of Conditional Beliefs", Journal of Philosophical Logic, vol. 25, 1996, p. 263--305.

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C. Boutilier,Iterated revision and minimal change of conditional beliefs, Journal of Philosophical Logic, 1996(25), 262-305.

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C. Boutilier,Iterated revision and minimal change of conditional beliefs, Journal of Philosophical Logic, 1996(25), 262-305.

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