ex8 - Only one student took Greek in spring 2001. The best...

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CS221 Exercise Set 8 1 CS 221, Autumn 2007 Exercise Set 8: Logic Review This week’s section will begin with an introduction to particle flters, a topic touched upon in Tuesday’s lecture, and which is potentially useFul For the vision project. We’ll then review frst-order logic in preparation For Tuesday’s lecture on knowledge representation. 1. Logic puzzle (Exercise 7.9 in Russell and Norvig, adapted From Barwise and Etchemendy (1993).) Given the Following, can you prove that the unicorn is mythical? How about magical? Horned? IF the unicorn is mythical, then it is immortal, but iF it is not mythical, then it is a mortal mammal. IF the unicorn is either immortal or a mammal, then it is horned. The unicorn is magical iF it is horned. 2. English to Logic (Adapted From exercises 8.6 and 8.7 in Russell and Norvig) Translate the Following sen- tences into frst-order logic, using a consistent vocabulary (which you must defne). Every student who takes ±rench passes it.
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Unformatted text preview: Only one student took Greek in spring 2001. The best score in Greek is always higher than the best score in rench. All Germans speak the same languages. 3. Valid and Satisfable Sentences (a) A set oF Formulas, { 1 , 2 , .... , n } is not consistent, iF and only iF: (A) the sentence 1 2 .... n is satisfable. (B) the sentence 1 2 .... n is valid. (C) the sentence 1 2 .... n is satisfable. (D) the sentence 1 2 .... n is valid. (b) Suppose F is satisfable, then it necessarily Follows that: (A) F is valid (B) F is valid (C) F is not satisfable (D) none oF the above (c) Assume ( F G ) is valid. Which oF the Following statements are true? i. Either F is valid or G is valid, but not necessarily both ii. F is valid and G is valid iii. F is satisfable or G is satisfable...
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