Notre Dame Journal of Formal Logic

On the Revision of Probabilistic Belief States

Craig Boutilier

Abstract

In this paper we describe two approaches to the revision of probability functions. We assume that a probabilistic state of belief is captured by a counterfactual probability or Popper function, the revision of which determines a new Popper function. We describe methods whereby the original function determines the nature of the revised function. The first is based on a probabilistic extension of Spohn's OCFs, whereas the second exploits the structure implicit in the Popper function itself. This stands in contrast with previous approaches that associate a unique Popper function with each absolute (classical) probability function. We also describe iterated revision using these models. Finally, we consider the point of view that Popper functions may be abstract representations of certain types of absolute probability functions, but we show that our revision methods cannot be naturally interpreted as conditionalization on these functions.

Article information

Source
Notre Dame J. Formal Logic Volume 36, Number 1 (1995), 158-183.

Dates
First available in Project Euclid: 19 December 2002

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1040308833

Mathematical Reviews number (MathSciNet)
MR1359112

Digital Object Identifier
doi:10.1305/ndjfl/1040308833

Zentralblatt MATH identifier
0844.03016

Subjects
Primary: 03B48: Probability and inductive logic [See also 60A05]
Secondary: 68T27: Logic in artificial intelligence 68T30: Knowledge representation

Citation

Boutilier, Craig. On the Revision of Probabilistic Belief States. Notre Dame Journal of Formal Logic 36 (1995), no. 1, 158--183. doi:10.1305/ndjfl/1040308833. http://projecteuclid.org/euclid.ndjfl/1040308833.


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