Computer Science 188 - Fall 1991 - Russell - Midterm 1

Computer Science 188 - Fall 1991 - Russell - Midterm 1 - CS...

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Unformatted text preview: CS 188 Fall 1991 Introduction to AI Stuart Russell Midterm examination You have 1 hr 20 min. The exam is open-book, open-notes. You will not necessarily nish all questions, so do your best ones rst. Write your answers in blue books. Hand them all in. Panic not. 1. (15 pts.) De nitions 2. (13 pts.) Search Provide brief, precise de nitions of the following: (a) Soundness (of an inference procedure) (b) Term (in predicate calculus) (c) Inheritance (d) Frame axiom (e) Admissible (algorithm) (a) (3) What elements are necessary to formally de ne a speci c search problem? (b) (5) De ne algebraic equation-solving (e.g., \Solve x2 y3 = 3 ; sin xy" for x) as a search problem. (You need to provide clearly-speci ed examples of each of the elements necessary for the de nition, but need not provide an exhaustive list). (c) (3) Give a reasonable heuristic function for equation-solving, and calculate its value for the state given in b). (d) (2) Would hill-climbing be an appropriate method for equation-solving using your heuristic? (a) (2) Inheritance information in semantic nets states that all members of a given class P have a particular value Y for a given slot Q. Write this as a rule in predicate calculus. (b) (3) Now consider the information content in Kelly's blue book: that, for example, 1973 Dodge Vans are worth $575. Suppose all this information (for 11,000 models) is encoded as logical rules, as in part a). Write down three such rules, including that for 1973 Dodge Vans. How would you use the rules to nd the value of a particular car (eg JB, which is a 73DodgeVan) given a backward-chaining theorem prover (such as prologx)? (c) (3) Compare the time e ciency of the backward-chaining method for solving this problem with the inheritance method used in semantic nets. (d) (3) Explain how forward chaining allows a logic-based system to solve the same problem e ciently, assuming that the KB contains only the 11,000 rules about price. (e) (2) Describe a situation in which neither forward nor backward chaining on the rules will allow the price query for an individual car to be handled e ciently. (f) (0) No credit: Can you suggest a solution enabling this type of query to be solved e ciently in all cases in logic systems? (As a hint, you might want to consider the fact that many semantic net systems inherit information from a prototype member of the class, e.g., Typical73DodgeVan.) 3. (13 pts.) Logic and semantic nets 4. (20 pts.) Situation-calculus planning In this question we will consider the problem of planning a route from one city to another. The basic action taken by the robot is (go x y) which takes it from city x to city y provided there is a direct route. (DirectRoute x y) is true i there is a direct route from x to y you can assume that all such facts are already in the KB. The robot begins in Savannah and must reach Gary. 1 (a) (b) (c) (d) (e) 5. (22 pts.) Lisp, Game-playing (1) Write a suitable logical description of the initial situation of the robot. (1) Write a suitable logical query whose solutions will provide possible paths to the goal. (3) Write a rule describing the go action. (2) Is a frame axiom needed? Why (not)? (8) Now suppose that following the direct route between two cities consumes an amount of fuel equal to the distance between the cities. The robot starts with fuel at full capacity. i. Augment your representation to include these considerations ii. write a new rule or rules describing the go action and iii. describe the initial situation. Your action description should be such that the query you speci ed above will still result in feasible plans. (f) (5) Now suppose some of the vertices are also gas stations, at which the robot can ll its tank using the (fillup) action. Extend your representation to include gas stations and write all the rules needed to completely describe the (fillup) action. (You can assume the robot doesn't have to worry about money.) The following code implements minimax search in a two-player game: (defun choose (side state limit) (the-biggest #'(lambda (s) (backed-up-value (opponent side) state 1 limit)) (successors state))) (defun backed-up-value (side state depth limit) (if (= depth limit) (evaluate side state) (apply (if (oddp depth) #'min #'max) (mapcar #'(lambda (s) (backed-up-value (opponent side) s (1+ depth) limit)) (successors state)))) (a) (3) (the-biggest f l) returns that item x in list l that has the highest value of (f x). Write the-biggest. (b) (3) In this and subsequent parts, we will consider the problem of search in a three-player game (you can assume no alliances are allowed for now). We will call the players 0, 1 and 2 for convenience. The rst change is that evaluate will return a list of three values, indicating (say) the likelihood of winning for players 0, 1 and 2 respectively. Copy and complete the following game tree by lling in the backed-up value triples for all remaining nodes: to move 0 ( ) 1 ( ) ( ) 2 ( ) ( ) ( ) ( ) 0 ( 1 2 3) ( 4 2 1) ( 6 1 2) ( 7 4 -1) ( 5 -1 -1) (-1 5 2) (7 7 -1) ( 5 4 5) (c) (11) Rewrite choose and backed-up-value so that they work correctly for the three-player game. choose should be rewritten in such a way that it generates an iterative deepening search (never mind why!). (You may de ne additional functions if needed. You may nd the-biggest useful also.) (d) (5) (open-ended) Discuss the problems that might arise if players could form and terminate alliances as well as make moves \on the board". Indicate brie y how these problems might be addressed. ...
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This note was uploaded on 05/17/2009 for the course CS 188 taught by Professor Staff during the Spring '08 term at University of California, Berkeley.

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