Notes


Belief change has been an active area of study in philosophy and, more recently, artificial intelligence. While probabilistic conditioning can be viewed as one approach to belief change, the study of the type of belief change considered in this chapter, where an agent must revise her beliefs after learning or observing something inconsistent with them, was essentially initiated by Alchourr n, G rdenfors, and Makinson, in a sequence of individual and joint papers. A good introduction to the topic, with an extensive bibliography of the earlier work, is G rdenfors's book Knowledge in Flux [1988]. AGM-style belief revision was introduced by Alchourr n, G rdenfors, and Makinson [1985]. However, similar axioms already appear in earlier work by G ardenfors [1978] and, indeed, also in Lewis's [1973] work on counterfactuals. This is perhaps not surprising, given the connection between beliefs and counterfactuals already discussed in Chapter 8. Interestingly, the topic of belief change was studied independently in the database community; the focus there was on how to update a database when the update is inconsistent with information already stored in the database. The original paper on the topic was by Fagin, Ullman, and Vardi [1983]. One of the more influential axiomatic characterizations of belief change—Katsuno and Mendelzon's notion of belief update [1991a]—was inspired by database concerns.

The presentation in this chapter is taken from a sequence of papers that Nir Friedman and I wrote. Section 9.1 is largely taken from [Friedman and Halpern 1997]; the discussion of belief change and the AGM axioms as well as iterated belief revision is largely taken from [Friedman and Halpern 1999] (although there are a number of minor differences between the presentation here and that in [Friedman and Halpern 1999]); the discussion of Markovian belief change is from [Friedman and Halpern 1996]. In particular, Propositions 9.1.1, 9.1.2, and 9.1.3 are taken from [Friedman and Halpern 1997], Theorems 9.3.5, 9.3.7, 9.4.1, 9.5.1, 9.5.2, and 9.5.3 are taken (with minor modifications in some cases) from [Friedman and Halpern 1999], and Theorem 9.6.2 is taken from [Friedman and Halpern 1996]. These papers also have references to more current research in belief change, which is still an active topic. I have only scratched the surface of it in this chapter.

Here are the bibliographic references for the specific material discussed in the chapter. Hansson [1999] discusses recent work on belief bases, where a belief base is a finite set of formulas whose closure is the belief set. Thinking in terms of belief bases makes it somewhat clearer how revision should work. The circuit diagnosis problem discussed has been well studied in the artificial intelligence literature (see [Davis and Hamscher 1988] for an overview). The discussion here loosely follows the examples of Reiter [1987b]. Representation theorems for the AGM postulates are well known. The earliest is due to Grove [1988]; others can be found in [Boutilier 1994; Katsuno and Mendelzon 1991b; G rdenfors and Makinson 1988]. Iterated belief change has been the subject of much research; see, for example, [Boutilier 1996; Darwiche and Pearl 1997; Freund and Lehmann 1994; Lehmann 1995; Levi 1988; Nayak 1994; Spohn 1988; Williams 1994]). Markovian belief change is also considered in [Boutilier 1998; Boutilier, Halpern, and Friedman 1998]. As I said in the text, Ramsey [1931a, p. 248] suggested the Ramsey test.




Reasoning About Uncertainty
Reasoning about Uncertainty
ISBN: 0262582597
EAN: 2147483647
Year: 2005
Pages: 140

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