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Main points of this exam paper are: Eight Queens Problem, Modelling, Implement, Order Predicate, Calculus Formulas, Refutation, Resolution, Lottery Prize, Lucky, Lottery Prize
Typology: Exams
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Instructions Answer exactly FOUR questions. SHOW ALL WORK.
Examiners: Dr. Jeanne Stynes Dr. Mel O’Cinneide Mr. Martin Donnelly
Q1. (a) Present two different ways of modelling the Eight Queens Problem and propose a solution for each approach. (15 marks) (b) Fully implement one of the solutions in (a) in Prolog. (10 marks)
Q2. (a) Transform the following expression into clause form: ( ∀ x ∃ y p(y,x) ) → ( ¬∃ x { ∀ y [ p(x,y) → q(x,y) ] } ) (7 marks) (b) Formulate the following as first order predicate calculus formulas and use the method of resolution and refutation to prove that “John is happy”. (8 marks) Any student who passes all his exams and wins a lottery prize is happy. Any student who studies or is lucky will pass all his exams. John did no study but he is lucky. Anyone who is lucky wins a lottery prize. (c) Explain why non-monotonic reasoning systems are used. Give at least two examples of how non-monotonic reasoning can be defined in such systems. (10 marks)
Q3. (a) Knowledge representation is an important aspect of problem solving. Justify this statement by presenting an example showing how an appropriate knowledge representation scheme can simplify the problem-solving process. (10 marks) (b) Briefly discuss the Dempster-Schafer OR the Mycin approach to handling uncertainty. Explain how uncertainty is propagated through the system, i.e., how are new uncertain beliefs/evidence combined? Illustrate with examples. (15 marks)
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Q4. (a) What are production systems? How are they used to solve problems? What factors influence the direction in which production rules are driven? Describe the typical problems encountered during the matching phase and explain how these could be overcome. (15 marks) (b) Write production rules to solve the following water jug problem: Jugs A, B, C have capacities of 8, 5 and 3 litres respectively. Assume the following constraints: A is initially full, B and C are empty; the jugs are irregularly shaped so that it is not possible to measure any intermediate amount; all or part of the contents of a jug may be poured into any other jug, but no new water may be added. Does there exist a sequence of pouring which leaves four litres of water in jug A? Show a trace of the problem-solving process. (10 marks)
Q5. (a) How are Game problems similar/different to State Space Search problems? (5 marks) (b) Outline in pseudocode the alpha-beta pruning algorithm for searching game trees. Describe at least three possible refinements to alpha beta pruning. (10 marks) (c) Consider the following game tree in which static scores are from the maximising player’s point of view. Which move should be chosen? Which nodes need not be examined in a left to right alpha-beta pruning? Which nodes need not be examined in a right to left alpha-beta pruning? (10 marks)
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e f g h i j k l
m n o s t u v w x y z a1 b1 c1 d 2 9 8 1 2 -6 -2 0 3 2 5 6 8 -4 7
p q r 14 7 9