# Affine arithmetic-type techniques for handling uncertainty in expert systems

#### Abstract

Expert knowledge consists of statements *S _{j}*:facts and rules. The expert's degree of confidence in each statement

*S*can be described as a (subjective) probability. For example, if we are interested in oil; we should look at seismic data (confidence 90%); a bank

_{ j}*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

*S*; computing

_{j}*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. The problem with this approach is that at each step, we ignore the dependence between the intermediate results

*F*; hence intervals are too wide. For example, the estimate for

_{j}*P*(

*A*∨ ¬

*A*) is not 1. ^ In this thesis, we propose a new solution to this problem; similarly to affine arithmetic, besides

*P*(

*F*), we also compute

_{j}_{P}(

*F*&

_{j}*F*) (or

_{i}*P*(

*F*

_{j}_{ 1}& ... &

*F*)), and on each step, use all combinations of

_{jk}*l*such probabilities to get new estimates. As a result, for the above stated e.g.,

*P*(

*A*∨ ¬

*A*) is estimated as 1. ^

#### Subject Area

Computer Science

#### Recommended Citation

Chopra, Sanjeev, "Affine arithmetic-type techniques for handling uncertainty in expert systems" (2005). *ETD Collection for University of Texas, El Paso*. AAI1430211.

https://digitalcommons.utep.edu/dissertations/AAI1430211