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SECOND INTERNATIONAL
SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

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Cornell University

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Ithaca, NY, USA

26 - 29 June 2001

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ELECTRONIC PROCEEDINGS

## Donald Bamber, I.R. Goodman

# Reasoning with Assertions of High Conditional Probability: Entailment with Universal Near Surety

### Abstract

Rules having rare exceptions are best interpreted as assertions of high conditional probability. In other words, a rule \emph{If $X$ then $Y$} is interpreted as meaning that $\Pr(Y|X) \approx 1$. In this paper, such rules are regarded as statements about imprecise probabilities, and imprecise probabilities are identified with convex sets of precise probabilities. A general approach to reasoning with such rules, based on second-order probability, is advocated. Within this general approach, different reasoning methods are needed, with the selection of a specific method being dependent upon what knowledge is available about the relative tightness of the approximation $\Pr(Y|X) \approx 1$ across rules. A method of reasoning, entailment with universal near surety, is formulated for the case when \emph{no} knowledge is available concerning these relative tightnesses. Finally, it is shown that reasoning via entailment with universal near surety is equivalent to carrying out a particular test on a directed graph.

** Keywords. ** Conditional probability, second-order probability, Bayesian inference, nonmonotonic logic, rule-based systems, threshold knowledge, informant, robustness, directed graph.

** Format. **PDF

**Paper Download **

The paper is availabe in the following sites:

** Authors addresses: **

Donald Bamber

SPAWARSYSCEN D44215

53345 RYNE ROAD

SAN DIEGO CA 92152-7251

USA

I.R. Goodman

Code D44215,Topside, Bldg. A33,

SPAWAR Systems Center,

San Diego, CA 92152

** E-mail addresses: **

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