Lecture 3 Uncertainty management in rulebased expert systems ■ Introduction, or what is uncertainty? ■ Basic probability theory ■ Bayesian reasoning ■ Bias of the Bayesian method ■ Certainty factors theory and evidential reasoning ■ Summary  Negnevitsky, Pearson Education, 2002 1 Introduction, or what is uncertainty? ■ Information can be incomplete, inconsistent, uncertain, or all three. In other words, information is often unsuitable for solving a problem. ■ Uncertainty is defined as the lack of the exact knowledge that would enable us to reach a perfectly reliable conclusion. Classical logic permits only exact reasoning. It assumes that perfect knowledge always exists and the law of the excluded middle can always be applied: IF A is true THEN A is not false  Negnevitsky, Pearson Education, 2002 IF A is false THEN A is not true 2 Sources of uncertain knowledge ■ Weak implications. Domain experts and knowledge engineers have the painful task of establishing concrete correlations between IF (condition) and THEN (action) parts of the rules. Therefore, expert systems need to have the ability to handle vague associations, for example by accepting the degree of correlations as numerical certainty factors.  Negnevitsky, Pearson Education, 2002 3 ■ Imprecise language. Our natural language is ambiguous and imprecise. We describe facts with such terms as often and sometimes, frequently and hardly ever. As a result, it can be difficult to express knowledge in the precise IF-THEN form of production rules. However, if the meaning of the facts is quantified, it can be used in expert systems. In 1944, Ray Simpson asked 355 high school and college students to place 20 terms like often on a scale between 1 and 100. In 1968, Milton Hakel repeated this experiment.  Negnevitsky, Pearson Education, 2002 4 Quantification of ambiguous and imprecise terms on a time-frequency scale Ray Simpson (1944) Term Always Very often Usually Often Generally Frequently Rather often Ab