Solutions: See Andrew Sawchuk's final plan obtained in his solutions to this problem.

Consider the following planning problem discussed in the textbook's slides and in class:

• Initial situation: At(Home) ∧ Sells(Supermarket,Milk) ∧ Sells(Supermarker,Bananas) ∧ Sells(HardwareStore,Drill)

• Final situation: Have(Milk) ∧ Have(Bananas) ∧ Have(Drill) ∧ At(Home)

• Actions:

  • Action: Go(p,q)
    Precondition: At(p)
    Effect: At(q) ∧ ¬At(p)

  • Action: Buy(x)
    Precondition: At(p) ∧ Sells(p,x)
    Effect: Have(x)

  Use the backward planning algorithm discussed in class to construct a plan to solve this problem. At each point in the construction of the plan, explicitly state:

  1. (2 points) what open condition you select;
  2. (10 points) how you fulfill that condition (either by the initial situation, an action already present in the plan, or a new action);
  3. (2 points) what variable instantiations are needed;
  4. (10 points) whether or not order constraints (promotion or demotion) between a newly added action and actions currently in the plan are needed;
  5. (6 points) when backtracking is needed to avoid failure.

  Show your work in detail.

Solutions: See Prof. Ruiz's solutions to this problem.

Consider the Bayesian net in Figure 14.21 (p. 560) of the Russell's and Norvig's textbook. Assume the prior and conditional probabilities given below:

• P(B) = 0.95
• P(R|B) = 0.8; P(R|¬B) = 0
• P(I|B) = 0.98; P(I|¬B) = 0
• P(G) = 0.65
• P(S|I∧G)=0.9; P(S|I∧¬G)=0; P(S|¬I∧G)=0; P(S|¬I∧¬G)=0
• P(M|S) = 0.7; P(M|¬S) = 0

Calculate the following conditional probabilities. Show in detail the process you follow to obtain your answer.

1. (12.5 points) (diagnosis) P(¬B|¬M)
2. (12.5 points) (causal inference) P(¬M|¬B)
3. (12.5 points) (intercausal inference) P(¬G|S∧I)
4. (12.5 points) (mixed inference) P(R∧G|I)