IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

26 - 29 June 2001

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:

- Gzipped file (Granada - Spain)
- Uncompressed file (Granada - Spain)
- Gzipped file (Gent - Belgium)
- Uncompressed file (Gent - Belgium)

** 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: **

Donald Bamber | bamber@spawar.navy.mil |

I.R. Goodman | goodman@spawar.navy.mil |

[ back to the Proceedings of ISIPTA '01 home page ]

Send any remarks to the following address: smc@decsai.ugr.es