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cial Arti Intelligence Name: Course Number: EXAMINATION FOR CIS 667/467, CSE 684, CIS 500 Fall 2001 ARTIFICIAL INTELLIGENCE Midterm Exam (Time allowed: ONE HOUR FIFTEEN MINUTES) NOTE: Print your name and course number! Write your answers clearly. Illegible answers will be considered incorrect. Unless mentioned, make your answers short and get to the point. Answers containing correct statements as well as incorrect statements will not get full points. 1. (4 pts) PSSH states that intelligence can be achieved through manipulations of physical symbols. It is important because symbolic AI (i.e., Logic based systems such as Expert systems) is based on this hypothesis. 2. (4 pts) Rational agents are sel sh agents. They take whichever action that maximizes the expected value of the performance measure given information they have. Being rational doesn t mean the agent will always choose the right action. It will choose the best action based on its best knowledge. 3. (5 pts) Prof. Marvin Minsky s the Perceptrons work. The Perceptron is a single-layer neural network. Minsky proved (along with Papert) that the Perceptron can t compute the XOR function. This means that the perceptron can t compute the universal logic, therefore it is incomplete. At that time, there was no algorithms that can train multi-layer neural network. In mid 80s, an algorithm called back-propagation was invented that can train multi-layer neural network. (Actually, the invention of the algorithm seems to be much earlier). 4. (5 pts) Goal-based agents have some sort of goal information. The information describes situations that are desirable. However, it does not have detailed information on how far the current state is to the goal state. It mearly knows what action will make it happy in a crude way. Utility-based agents on the other hand can compute usefulness i.e., utility of themselves for a given state. Utility is a function that maps a state to a real number, which describes associate degree of happiness of the agents. Using utility, agents can compute the distance between the current state to the goal-state more precise manner than Goal-based agents. 5. (2+2+2 pts) Explain di erent environment types in the following: CONTINUED 2 Arti cial Intelligence (a) Accessible vs. Inaccessible In an accessible environment, agents can perceive the complete state of the environment. Inaccessible environment doesn t allow it. (b) Search space vs. State space. Search space is the problem space itself. State space is an abstraction of given search space that represents all possible states for the search space in order to solve given problem. (c) Episodic vs. Non-Episodic If the environment can be divided into indpendent episodes it is episodic. Othewise, it is nonepisodic 6. (6 pts) (1) Parent-node is necessary to backtrack to current node s parent. (2) after reaching to the goal state, to retrieve the path from the initial state to the goal state In A search, backtracking is necessary to expand nodes in monotonically increasing manner in terms of f (n). In A , path-max algorithm needs this info. In some search algorithms, not all expanded nodes are stored in the queue, therefore the parent node information is needed. 7. (6 pts) State di erence between a singe-state problem and a multi-state problem. Hint: think of problems as the environment types we discussed. Single-state problem: The environment is deterministic and accessible. Vacuum world with sensor input that can observe all the squares. Multi-state problem: environment The is deterministic but inaccessible. Vacuum world without sensor input. 8. (5 pts) We discussed that at least one direction of a bi-directional search must be a breadth- rst search. What would be a good choice for the other direction. Why? Either BFS or IDS. We can t use DFS since the two algorithms still can miss each other. Timing is everything. 9. (4 + 4 + 4 + 4 pts) (a) Depth-limited search. We know the depth of the goal. There is only one goal. the goal-state and path from the initial state to the goal state are returned. (b) IDS. The state space is large so BFS is not good. The state space may be in nite, so DFS can get stuck in a in nite path. the goal-state and path from the initial state to the goal state are returned. (c) SA. The goal state is not known. So we can use any other algorithm except SA and uniform random search. Since we can compare given any two states, SA is a good candidate. A goal-state is returned. It may or may not be true goal-state. CONTINUED 3 Arti cial Intelligence (d) A*. Since we have heuristic function. A* is optimal and complete. 10. (3 + 3 pts) (a) SA and RRH are similar in that both are gradient search algorithms. However, SA allows occasional bad moves while RRH always take a better state among the candidates. (b) For a large T , the probability of taking bad move is high. For a large E the prob. is smaller. I.e., taking a big bad jump has smaller prob. 11. (2 + 2 pts) (a) Probability theory: Facts; Fuzzy logic: degree of truth. (b) Probability theory: the prob. of rain tomorrow is 0.9; Fuzzy logic: Syracuse is a large city has degree of truth 0.1. 12. (2 + 2 + 3) (a) (1) Problem in representing quantitities. (2) Frame problem: representing non-changes and changes in the environment (b) Quati ers (c) The frame problem. One can alleviate (or solve) using extension of FOL. Situation calculus is one way. 13. (2 + 2 pts) Inference procedure. KB i means sentence can be derived from KB by procedure i. (a) What does it mean by i is sound? Soundness means truth-preserving. Given a knowledge base KB, an inference procedure i generates only sentences that are entailed by KB. I.e., whenever KB i , it is true that KB |= . (b) What does it mean by i is complete? Whenever KB |= , it is true that KB sentences entailed by KB. 14. (10 pts) Prove P3,1 . Currently, in KB, we have: B1,1 , B2,1 , B1,2 . Rules: B2,1 P1,1 P2,2 P3,1 P2,1 B1,1 P1,2 P2,1 P1,1 B1,2 P1,3 P1,2 P2,2 P1,1 Using B2,1 from KB and Modus Ponens, we have P1,1 P2,2 P3,1 P2,1 Using B1,1 from KB and Modus Ponens and And-Elimination, we have, P 1,2 , P2,1 , P1,1 CONTINUED i . That is, the inference procedure i generates all 4 Arti cial Intelligence Using B1,2 from KB and Modus Ponens and And-Elimination, we have, P 1,3 , P1,2 , P2,2 , P1,1 Using P1,1 P2,2 P3,1 P2,1 and Unit Resolution with P1,1 , P2,1 , and P2,2 , we have P3,1 left. 15. (3 + 3 + 3 + 4 pts) Convert the following English sentences in FOL (a) One s mother is one s female parent x, yM other(x) F emale(x) P arent(x, y) Child(y) or m, cM other(c) = m F emale(m) P arent(m, c) (b) Some mothers stay home xM other(x) Home(x) (c) Every mother loves her child x, yM other(x) ChildOf (y, x) Loves(x, y) (d) Every mother is either a housewife or working woman but not both xM other(x) (house wif e(x) working(x)) ( house wif e(x) working(x))

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