Inference Net

The fundamental knowledge base for a rule-based diagnostic expert system is expressed by rules in the form

meaning if evidence holds then hypothesis holds. The validity of hypothesis is inferred from the validity of evidence.

However, as you can imagine, there can be uncertainty both in the rules (expressed by the expert) and in the data (provided by user). That's why the early expert systems started to use "probabilities". Even when the statistical methods are used to compute with those "probabilities", they are just subjective estimates, not objective probabilities in a statistical meaning.

The need for uncertainty handling was recognized early when the first expert systems were constructed. Famous examples are MYCIN and PROSPECTOR. MYCIN was intended for medical applications to help with treating blood infections, in particular to identify bacteria causing severe infections. PROSPECTOR attempted to represent the knowledge and reasoning process of geological experts and as such predicted unknown molybdenum deposit which was a huge commercial success that lead in strong interest in expert systems development. The PROSPECTOR expert system used the following form of the rules to express uncertainty:

This rule, provided by an expert, means (don't worry if you don't understand, just continue with next paragraph and return here later): "If the presumption (evidence) E certainly holds then accept the conclusion H with measure (probability) P(H|E); if the negation of E certainly holds then accept the conclusion H with measure P(H|¬E)”. E and H are statements (hypotheses). P(H|E) (probability of H when E holds) and P(H|¬E) are subjective conditional probabilities. P(H|E) is called sufficiency measure of the rule while P(H|¬E) is called necessity measure of the rule. These measures express uncertainty in the knowledge base.

The rules (i.e., the content of the knowledge base) can be represented in a graphical manner. See the example below for the rules, in fact the whole knowledge base for the simple example you have explored in the previous step. Try to click on the nodes and explore the rules.

In particular, find and observe the rule

which means - if the car stars OK, then the expert says that there is low probability it will need to be checked. It the car doesn't start OK, then the expert says that there is much higher probability (but not certainty in this case) that the car will need a check. How did we found the rule and the numbers for the knowledge base? In general, we asked an expert, who provided the rule and also estimated the "probabilities". Note that if we would have exact probabilities, not estimates, we would not need an expert system - we would have exact mathematic model of the problem.