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Taking levi identity seriously: a plea for iterated belief contraction

Intelligent behaviour assumes that when an agent receives a new piece of information (an observation, a piece of evidence), it can accommodate it into its current stock of beliefs in a rational fashion. Under the simplifying assumption that the observation has been checked out and should be "accepted", a problem arises if it conflicts with the current stock of beliefs. Naturally, some of the current beliefs have to jettisoned in order to make room for the new observation. Reason dictates that such loss of information should be minimised. But typically there are far too many ways of doing it. The problem of belief contraction involdes investigating the rational ways of discarding some information from one's belief corpus. The classical account of belief change provides a framework for "one-shot" belief contraction (and belief revision); but it leaves open the issue of how an agent can perform a sequence of belief contractions in a rational manner. This talk discusses why it is important to have an account of iterated belief contraction, and suggests one interesting way of doing it. Most work on iterated belief change has focused on iterated belief revision, namely how to compute (K*x)*y. Historically however, belief revision can be defined in terms of belief expansion and belief contraction, where expansion and contraction are viewed as primary operators. Accordingly, our attention to iterated belief change should be focused on constructions like (K+x)+y, (K-x)+y, (K+x)-y and (K-x)-y. The first two of these are relatively straightforward, but the last two are more problematic. Here we consider these latter, and formulate iterated belief change by employing the Levi identity and the Harper Identity as the guiding principles.

Citation

A. Nayak, R. Goebel, M. Orgun, T. Pham. "Taking levi identity seriously: a plea for iterated belief contraction". International Conference on Knowledge Science (ICKS), pp 211-220, August 2006.

Keywords: machine learning
Category: In Conference

BibTeX

@incollection{Nayak+al:ICKS06,
  author = {Abhaya Nayak and Randy Goebel and Mehmet Orgun and T. Pham},
  title = {Taking levi identity seriously: a plea for iterated belief
    contraction},
  Pages = {211-220},
  booktitle = {International Conference on Knowledge Science (ICKS)},
  year = 2006,
}

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