1 / 8

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:

tuvya
Download Presentation

Section 6

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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”!

More Related