License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.07351.22
URN: urn:nbn:de:0030-drops-12404
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2007/1240/
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Rott, Hans

Two-Dimensional Belief Change

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07351.RottHans.Paper.1240.pdf (0.3 MB)

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:DagSemProc.07351.22,
  author =	{Rott, Hans},
  title =	{{Two-Dimensional Belief Change}},
  booktitle =	{Formal Models of Belief Change in Rational Agents},
  pages =	{1--27},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7351},
  editor =	{Giacomo Bonanno and James Delgrande and J\'{e}r\^{o}me Lang and Hans Rott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2007/1240},
  URN =		{urn:nbn:de:0030-drops-12404},
  doi =		{10.4230/DagSemProc.07351.22},
  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
Collection: 07351 - Formal Models of Belief Change in Rational Agents
Issue Date: 2007
Date of publication: 22.11.2007

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