Iterable AGM Functions

C. Areces and V. Becher. Iterable AGM Functions. In H. Rott and M. Williams, editors, Frontiers in Belief Revision, Applied Logic Series, pp. 261–277, Kluwer Academic Publishers, 2001. Extended version of ``Iterable AGM Functions'' (Areces and Becher).

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Abstract

The AGM model [Alchourrón et al., 1985] has been criticized for not ad- dressing the problem of iterated change. This is true, but in some cases the invalid claim that “AGM does not allow iteration” has been made. In this paper we examine the most elementary scheme of iteration: a binary operation * defined for any theory K and any formula α. We naturally extend the AGM model showing that it is in fact compatible with iteration. Following Alchourrón and Makinson’s early reference to an iterated form of the safe contraction function, we provide extended constructions for each of the five AGM presentations (meet functions, systems of spheres, postulates, epistemic entrenchments and safe hierarchies) and prove their equivalence.

BibTeX

@InCollection{Areces2001,
  author =       "C. Areces and V. Becher",
  booktitle =    "Frontiers in Belief Revision",
  publisher =    "Kluwer Academic Publishers",
  title =        "Iterable {AGM} Functions",
  abstract =     "The AGM model [Alchourrón et al., 1985] has been
                 criticized for not ad- dressing the problem of iterated
                 change. This is true, but in some cases the invalid
                 claim that “AGM does not allow iteration” has been
                 made. In this paper we examine the most elementary
                 scheme of iteration: a binary operation * defined for
                 any theory K and any formula α. We naturally extend
                 the AGM model showing that it is in fact compatible
                 with iteration. Following Alchourrón and Makinson’s
                 early reference to an iterated form of the safe
                 contraction function, we provide extended constructions
                 for each of the five AGM presentations (meet functions,
                 systems of spheres, postulates, epistemic entrenchments
                 and safe hierarchies) and prove their equivalence.",
  year =         "2001",
  editor =       "H. Rott and M. Williams",
  note =         "Extended version of ``Iterable AGM Functions'' (Areces
                 and Becher).",
  pages =        "261--277",
  series =       "Applied Logic Series",
  volume =       "22",
  ISBN =         "978-90-481-5720-4",
}