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Section 6

Section 6. Exam Review. Search. Assume we have D different admissible heuristics, . Which of the following heuristics are also admissible ? a, c, d Which one do you think is best? d, since it’s an upper bound of the others, and still admissible a. b. c. d. . Search. True or False:

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Section 6

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  1. Section 6 Exam Review

  2. Search • Assume we have D different admissible heuristics, . Which of the following heuristics are also admissible? • a, c, d • Which one do you think is best? • d, since it’s an upper bound of the others, and still admissible a. b. c. d.

  3. Search • True or False: • A* expands all nodes with F(n)<C • True! It has to expand them otherwise it won’t have the optimality guarantee • A* expands all nodes with F(n)<=C • False! It might expand only some of those, as it can stop when expanding the goal • IDS is optimal if step-cost is a constant, the search-state is finite and a goal exists • True!

  4. Games A B C D E F G H Max Min • Assuming that we run minimax with alpha-beta pruning, expanding from left to right: • Is it possible to assign values to A and B, such that node C will be pruned? • No! we will always have to expand C • Is it possible to assign values to nodes A, B and C, such that node D will be pruned? • Yes! For example, try A = 6, B=1, C = 7 Max

  5. KR • Transform the following formula into conjunctive normal form: • x P(x)Q(x) • Remove implication: x ¬P(x) ∨ Q(x) • Eliminate universals: ¬P(x) ∨ Q(x) • y P(y)  R(y) • Existential instantiation: P(c) R(c), where c is a skolem constant

  6. KR • Which of the following rules are sound? Explain your answer using the formal concepts of entailment, satisfiability and validity. Hint: think about truth tables and models. • From , infer  • Sound: every model that makes  true, also makes  true. Formally, we have  |=  • From , infer  • Not sound! For example, if  is false and  is true, then  is true, but  is false

  7. KR • Suppose F is satisfiable. Then which of the following statements are true?a.  F is validb. (not F) is validc. (not F) is not satisfiable • Solution • (a) is false. For F to be valid, it needs to be true in any model. We only know that it’s true in at least one model • (b) is false. We know that not F is false in at least one model (the one that satisfies F) • (c) is false. We know that F is satisfiable by some model, this doesn’t mean that there isn’t a (different) model that satisfies not F • Note that if F was valid, we would have had that (not F) is not satisfiable

  8. KR • Can the following sentences be represented by First-order Logic and/or Description Logic? 1. At Harvard, computer science graduate students are SEAS graduate students, who belong to GSAS graduate students. - FOL: x (CS-grad(x)SEAS-grad(x))(SEAS-grad(x)GSAS-grad(x)) - Description logic: CS-grad SEAS-grad GSAS-grad • 1/7 of SEAS graduate students are computer science graduate students. - Neither FOL or DL can express “1/7”!

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