Iterable AGM Functions

C. Areces and V. Becher. Iterable AGM Functions. In Proceedings of BR'98. Belief Revision Workshop, Trento, Italy, 1998.

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Abstract

The AGM model has been criticized for not addressing 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: an iterable function. We formulate an iterable version of the AGM model, showing that the AGM formalism is in fact compatible with iteration. Following Alchourron and Makinson's early reference to an iterable form of a safe contraction function, we give an iterable construction for each of the ve AGM presentations (meet functions, systems of spheres, postulates, epistemic entrenchments and safe hierarchies) and prove their equivalence.

BibTeX

@InProceedings{Areces1998,
  author =       "C. Areces and V. Becher",
  booktitle =    "Proceedings of {BR'98}. Belief Revision Workshop",
  title =        "Iterable {AGM} Functions",
  abstract =     "The AGM model has been criticized for not addressing
                 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: an iterable
                 function. We formulate an iterable version of the AGM
                 model, showing that the AGM formalism is in fact
                 compatible with iteration. Following Alchourron and
                 Makinson's early reference to an iterable form of a
                 safe contraction function, we give an iterable
                 construction for each of the ve AGM presentations (meet
                 functions, systems of spheres, postulates, epistemic
                 entrenchments and safe hierarchies) and prove their
                 equivalence.",
  year =         "1998",
  address =      "Trento, Italy",
}