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For Monday

For Monday. Read Chapter 13 Chapter 11, exercise 4. Program 3. Homework. Example. Op( Action: Go(there); Precond: At(here); Effects: At(there), ¬At(here) ) Op( Action: Buy(x), Precond: At(store), Sells(store,x); Effects: Have(x) ) A 0 :

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For Monday

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  1. For Monday • Read Chapter 13 • Chapter 11, exercise 4

  2. Program 3

  3. Homework

  4. Example Op( Action: Go(there); Precond: At(here); Effects: At(there), ¬At(here) ) Op( Action: Buy(x), Precond: At(store), Sells(store,x); Effects: Have(x) ) • A0: • At(Home) Sells(SM,Banana) Sells(SM,Milk) Sells(HWS,Drill) • A¥ • Have(Drill) Have(Milk) Have(Banana) At(Home)

  5. Example Steps • Add three buy actions to achieve the goals • Use initial state to achieve the Sells preconditions • Then add Go actions to achieve new pre-conditions

  6. Handling Threat • Cannot resolve threat to At(Home) preconditions of both Go(HWS) and Go(SM). • Must backtrack to supporting At(x) precondition of Go(SM) from initial state At(Home) and support it instead from the At(HWS) effect of Go(HWS). • Since Go(SM) still threatens At(HWS) of Buy(Drill) must promote Go(SM) to come after Buy(Drill). Demotion is not possible due to causal link supporting At(HWS) precondition of Go(SM)

  7. Example Continued • Add Go(Home) action to achieve At(Home) • Use At(SM) to achieve its precondition • Order it after Buy(Milk) and Buy(Banana) to resolve threats to At(SM)

  8. Uncertainty • Everyday reasoning and decision making is based on uncertain evidence and inferences. • Classical logic only allows conclusions to be strictly true or strictly false • We need to account for this uncertainty and the need to weigh and combine conflicting evidence.

  9. Coping with Uncertainty • Straightforward application of probability theory is impractical since the large number of conditional probabilities required are rarely, if ever, available. • Therefore, early expert systems employed fairly ad hoc methods for reasoning under uncertainty and for combining evidence. • Recently, methods more rigorously founded in probability theory that attempt to decrease the amount of conditional probabilities required have flourished.

  10. Probability • Probabilities are real numbers 0­1 representing the a priori likelihood that a proposition is true. P(Cold) = 0.1 P(¬Cold) = 0.9 • Probabilities can also be assigned to all values of a random variable (continuous or discrete) with a specific range of values (domain), e.g. low, normal, high. P(temperature=normal)=0.99 P(temperature=98.6) = 0.99

  11. Probability Vectors • The vector form gives probabilities for all values of a discrete variable, or its probability distribution. P(temperature) = <0.002, 0.99, 0.008> • This indicates the prior probability, in which no information is known.

  12. Conditional Probability • Conditional probability specifies the probability given that the values of some other random variables are known. P(Sneeze | Cold) = 0.8 P(Cold | Sneeze) = 0.6 • The probability of a sneeze given a cold is 80%. • The probability of a cold given a sneeze is 60%.

  13. Cond. Probability cont. • Assumes that the given information is all that is known, so all known information must be given. P(Sneeze | Cold Ù Allergy) = 0.95 • Also allows for conditional distributions P(X |Y) gives 2­D array of values for all P(X=xi|Y=yj) • Defined as P (A | B) = P (A Ù B) P(B)

  14. Axioms of Probability Theory • All probabilities are between 0 and 1. 0  P(A)  1 • Necessarily true propositions have probability 1, necessarily false have probability 0. P(true) = 1 P(false) = 0 • The probability of a disjunction is given by P(A  B) = P(A) + P(B) - P(A ÙB)

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