Expert Systems Reasonable Reasoning

The good and the bad

• Forward chaining allows you to conclude anything
• Forward chaining is expensive
• Backward chaining requires known goals.
• Premises of backward chaining directs which facts (tests) are needed.
• Rule trace provides explanation.

Simple Confidence Calculus

• This will yield an intuitive degree of belief in system conclusion.
• To each fact, assign a confidence or degree of belief. A number between 0 and 1.
• To each rule, assign a rule confidence: also a number between 0 and 1.

• Confidence of premise of a rule =
• Minimum confidence of each condition
• Intuition: strength of argument is weakest link
• Confidence in conclusion of a rule =
• (confidence in rule premise)*(confidence in rule)
• Confidence in conclusion from several rules: r1,r2,..rm with confidences c1,c2,..cm =
• c1 @ c2 @... cm
• Where x @ y is 1- (1-x)*(1-y).

And now with confidences

• Facts:
• F1: Ungee gives milk: .9
• F2: Ungee eats meat: .8
• F3: Ungee has hoofs: .7
• Rules:
• R1: If X gives milk, then it is a mammal: .6
• R2: If X is a mammal and eats meat, then carnivore: .5
• R3: If X has hoofs, then X is carnivore: .4

• R1 with F1: Ungee is mammal. (F4)
• Confidence F4: C(F4) = .9*.6 = .54
• R2 using F2 and F4 yields: Ungee is carnivore (F5).
• C(F5) from R2 = min(.54, .8)*.5 = .27
• R3 using F3 conclude F5 from R3
• C(F5) from R3 = .7*.4 = .28
• C(F5) from R3 and R2 = .27 @ .28 = 1 –(1-.28)*(1-.27) = .48

Problems and Counters-Arguments

• People forget to say the obvious
• Rules difficult to acquire (years)
• People don’t have stable or correct estimates of “confidence”
• Data insufficient to yield good estimate of true probabilities.
• But Feigenbaum: In the knowledge lies the power.
• Calculus/confidences not that important

AI Winter

• Expert Systems found useful
• hundreds of successful systems
• Consultants and hype ->
• Hundreds of unsucessful systems
• Remember:
• needs an expert
• Knowledge needs to be representable as rules
• Now on to Probability based approach