Artificial Intelligence Problem Set 3 Assigned: Oct. 13 Due: Oct. 20 Problem 1 For each of the ambiguities listed below, explain how it can be disambiguated using either selectional restrictions, frequency in context (for lexical ambiguity), or world knowledge. If disambiguation is possible using selectional restrictions, you should prefer this to the other two, as selectional restrictions are usually both stronger and easier to implement. If you use selectional restriction, explain what are the features, the relation, and the constraint involved. If you use frequency in context, explain how the context is established by other parts of the sentence. If you use world knowledge, explain the rules being used. For example: \begin{itemize} \item The *bat* ate its dinner'' [= flying mammal rather than wooden club]. Answer: Selectional restrictions. The subject of ate'' must be ANIMATE: wooden club'' is not ANIMATE. \item I went up to the door of the house *with the red shutters*'' [with the red shutters'' is attached to house'' not door'' or went''.] Answer: World knowledge. Shutters are part of a house, not part of a door. It is unusual to go places carrying shutters. \item In the seventh inning, the *pitcher* was replaced''. [pitcher'' = baseball player rather than container.] Answer: Frequency in context. The word inning'' establishes the context as baseball. Problems A. The cat *lies*& on the rug. (lies" = lies down"). B. The politician *lies* about his opponent's record. (lies" = tells falsehoods".) C. While trying out the new compiler, I found a *bug*. (Bug" = error in a program.'') D. While cleaning the kitchen, I found a *bug*. (Bug'' = insect''.) E. We stopped at a restaurant for dinner. *It* was delicious. F. We stopped at a restaurant for dinner. *It* was noisy and crowded. G. I looked for my sweater in the closet, but *it* wasn't there. (It'' = sweater.) H. I looked for my sweater in the closet, but *it* was so messy that I couldn't find *it*. (First it'' = closet, second it'' = sweater.) \pagebreak {\bf Problem 2:} Suppose that you are interpreting a speech signal consisting of three words. The speaker is enunciating very carefully, so you are sure that the first word is either "great" or "grate"; that the second is either "blue" or "blew", and that the third is either "whale" or "wail". You are using a bigram model of language with the following Markov model: 0.9 0.7 great---->blue------>whale / \ / \ / 0.8 / 0.1 \ / \ /0.4 / \/ \ / START /\ X \ 0.4 / \ / \0.3 0.2 \ / \ / \ grate----->blew---->wail 0.6 0.6 A. What are the probabilities of the various interpretations, great blue whale'', great blue wail'', great blew whale'', great blew wail'', grate blue whale'', grate blue wail'', grate blew whale'', grate blew wail''? Which is the most likely interpretation? Note: You may omit the normalization factor (the denominator "P(s1,s2,s3).") B. Suppose that the speaker is speaking a dialect in which there are slight difference between the pronounciation of each pair of homophones. (that is, "great" is pronunouced slightly differently from "grate", and so on.) Let S1, S2, S3 be the sounds that the speaker makes for the three words. Suppose that we have the following probabilities: P(S1 | "great") = 0.3. \\ P(S1 | "grate") = 0.5. \\ P(S2 | "blue") = 0.6. \\ P(S2 | "blew") = 0.6. \\ P(S3 | "whale") = 0.2 \\ P(S3 | "wail") = 0.8 What now are the probabilities of various interpretations? Which is the most likely interpretation? C. What independence assumptions are you making in (B)?