Affine arithmetic-type techniques for handling uncertainty in expert systems
Expert knowledge consists of statements Sj:facts and rules. The expert's degree of confidence in each statement S j 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 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. The problem with this approach is that at each step, we ignore the dependence between the intermediate results Fj; hence intervals are too wide. For example, the estimate for P(A ∨ ¬A) is not 1. In this thesis, we propose a new solution to this problem; similarly to affine arithmetic, besides P(Fj), we also compute P(Fj & Fi) (or P(Fj 1 & ... & Fjk)), and on each step, use all combinations of l such probabilities to get new estimates. As a result, for the above stated e.g., P(A ∨ ¬A) is estimated as 1.
Chopra, Sanjeev, "Affine arithmetic-type techniques for handling uncertainty in expert systems" (2005). ETD Collection for University of Texas, El Paso. AAI1430211.