# Interval-Type and Affine Arithmetic-Type Techniques for Handling Uncertainty in Expert Systems, with Applications to Geoinformatics and Computer Security

## Publication Date

8-2005

UTEP-CS-04-37b.

Short version published in the Proceedings of the 17th World Congress of the International Association for Mathematics and Computers in Simulation IMACS'2005, Paris, France, July 11-15, 2005; full paper published in Journal of Computational and Applied Mathematics, 2007, Vol. 199, No. 2, pp. 403-410.

## Abstract

Expert knowledge consists of statements Sj (facts and rules). The expert's degree of confidence in each statement Sj can be described as a (subjective) probability (some probabilities are known to be independent). Examples: if we are interested in oil, we should look at seismic data (confidence 90%); a bank A trusts a client B, so if we trust A, we should trust B too (confidence 99%). If a query Q is deducible from facts and rules, what is our confidence p(Q) in Q? We can describe Q as a propositional formula F in terms of Sj; computing p(Q) exactly is NP-hard, so heuristics are needed.

Traditionally, expert systems use technique similar to straightforward interval computations: we parse F and replace each computation step with corresponding probability operation. Problem: at each step, we ignore the dependence between the intermediate results Fj; hence intervals are too wide. Example: the estimate for P(A\/~A) is not 1. Solution: similarly to affine arithmetic, besides P(Fj), we also compute P(Fj & Fi) (or P(Fj & ... & Fk)), and on each step, use all combinations of l such probabilities to get new estimates. Results: e.g., P(A\/~A) is estimated as 1.

tr04-37a.pdf (107 kB)
Updated version: UTEP-CS-04-37a

tr04-37.pdf (167 kB)
Original file: UTEP-CS-04-37

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