- Probability
- why do we need in AI ?
- insufficient knowledge (laziness?)
- hidden variables
- e.g. to differentiate between capital and small letters with no absolute size
- truly stochastic systems
- e.g. quantum mechanics, competing with humans
- interpretations of probability
- relative frequency of repeating phenomenon
- Bayesian interpretation (see below)
- actual meaning in nature
- subjective degree of belief
- example: what is the probability of the sun exploding today?
- undefined since hasn't happened yet
- zero since in all tests so far it hasn’t happened
- p < 1/D where D is age of sun in days
- determinable from statistics of other similar stars in universe
- axioms of probability theory
- range 0 <= p <= 1
- limits p(T) = 1 p(F) = 0
- conditional probability p(A|B) = p(A And B) / p(B)
- A and B are independent if p(A|B) = p(A) ie. p(A And B) = p(A) p(B)
- prove by p(A) + p(not A) = 1
- disjunction p(A Or B) = p(A) + p(B) - p(A And B)
- mutually exclusive if P(A And B) = 0 i.e. p(A or B) = p(A) + p(B)
- Bayes p(H
_{i}|E) = p(E|H_{i}) p(H_{i}) / S_{i}p(E|H_{i}) p(H_{i}) - use to define probabilities without relative frequency
- Expert Systems that use probability
- if - then rules are replaced by conditional probabilities
- probabilities must be provided by the expert
- e.g. PROSPECTOR knows:
- prior probability for finding various minerals
- probability that if there is a given mineral then given evidence appears
- we need the probability - if evidence appears then mineral
- stock market expert example
- SR = stock market rises
- SF = stock market falls
- IR = interest rates rise
- IF = interest rates fall
- DR = dollar rises
- DF = dollar falls
- we want to know p(SR)
- p(SR) = p(SR|IR) p(IR) + p(SR|IF) p(IF)
- we need p(IR) (and then p(IF) = 1 - p(IR))
- p(IF) = p(IF|DR) p(DR) + P(IF|DF) p(DF)
- we need p(DR) (and then p(DF) = 1 - p(DR)) so we backtrack
- expert has preprogrammed values of p(X|Y)
- user must enter an estimate of p(DR) to get p(SR)
- Fuzzy Logic
- note the difference between:
- probabilistic case: 100 cups of which 90% coffee and 10% tea
- fuzzy case: 100 cups with 90% coffee and 10% tea in them
- fuzzy measure m(A)
- m(Not A) = 1 - m(A)
- m(A And B) = min( m(A), m(B) )
- m(A Or B) = max( m(A), m(B) )
- no need for normalization
- Final thoughts
- ethical questions
- it becomes clear that humans are not so special
- perhaps machines may be developed that will one day destroy humans
- legal questions
- if expert sustem passes Turing test will it deserve human rights?
- when physician uses a medical expert system, who is liable for malpractice?
- in US today ES is considered by courts to be like a textbook
- if ES provable to be better than MD, then perhaps he will be liable if doesn’t follow its advice
- if financial ES deals with stocks and bonds is owner liable for debts?
- can ES own assets and deal on its own behalf?
- ES car driver can legally exceed spped limit (but designer will be liable for damages)
- philosophical questions
- strong AI
- must a Turing test expert system be conscious ?
- brain prosthesis thought experiment
- replace neurons one at a time
- at end entire brain is artificial
- equivalently we could replace brain with a lookup table
- Have we really learned anything about AI ?
- Projects
- 1) any conversant program
- 2) any microworld agent
- 3) any artificial life program
- 4) any game playing program
- 5) any learning system
- 6) any expert system (car fault diag, internet searching, integration, from your work)
- 7) theorem prover (geometry, trig, word problems)
- 8) heuristic builder
- 9) test (default)