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URN: urn:nbn:de:0030-drops-12404
URL: http://drops.dagstuhl.de/opus/volltexte/2007/1240/
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Rott, Hans

Two-Dimensional Belief Change

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Abstract

The idea of two-dimensional belief change operators is that a belief state is transformed by an input sentence $A$ in such a way that $A$ gets accepted with at least the strength or certainty of a sentence $B$ (the reference sentence). The input of such a transformation may alternatively be conceived as `$B leq A$' [`$B$ less-than-or-equal-to $A$']. This notation makes explicit that the process induced is basically one of doxastic preference change. The principal case of two-dimensional belief change obtains when $B$ is a prior belief which is more strongly accepted than both $A$ and $ eg A$, but the non-principal cases are interesting in their own right. Various two-dimensional revision operators were studied by Cantwell (1997, `raising' and `lowering'), Fermé and Rott (2003, `revision by comparison'), and Rott (2007, `bounded revision'). Special choices of a fixed input sentence $A$ or a fixed reference sentence $B$ lead to some well-known unary oparators of belief change: `irrevocable' (aka `radical') revision, `severe withdrawal' (aka `mild contraction'), `natural' (aka `conservative') and `lexicographic' (aka `moderate') revision. The talk gives a survey of several variants of two-dimensional belief change and their representations. I argue that two-dimensional belief change operators offer an interesting qualitative model with an expressive power between (all too poor) unary operators and (all too demanding) quantitative models of belief change.

BibTeX - Entry

@InProceedings{rott:DSP:2007:1240,
  author =	{Hans Rott},
  title =	{Two-Dimensional Belief Change},
  booktitle =	{Formal Models of Belief Change in Rational Agents},
  year =	{2007},
  editor =	{Giacomo Bonanno and James Delgrande and J{\'e}r{\^o}me Lang and Hans Rott},
  number =	{07351},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2007/1240},
  annote =	{Keywords: Belief revision, radical revision, conservative revision, moderate revision, severe withdrawal, preference change, qualitative vs. quantitative change}
}

Keywords: Belief revision, radical revision, conservative revision, moderate revision, severe withdrawal, preference change, qualitative vs. quantitative change
Seminar: 07351 - Formal Models of Belief Change in Rational Agents
Issue Date: 2007
Date of publication: 22.11.2007


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