### CS534 Artificial Intelligence Homework 5 - Fall 2007

#### PROF. CAROLINA RUIZ

Due Date: Part I on October 18 and Part II on October 25, 2007

• Read Chapters 8 and 9 of the textbook.

• Problems: You need to turn in written solutions ONLY TO THE PROBLEMS MARKED WITH ONE ASTERISK "*" BELOW at the beginning of class when the homework is due. Solve the other problems before the class also so that you can ask questions about them in preparation for Exam 2. Remember to show your work and explain your answers.

1. Chapter 8 (due on October 18th): 8.4*, 8.6*, 8.7*, 8.8, 8.12

2. Chapter 9 (due on October 25th): 9.4*, 9.7, 9.9, 9.19*

3. * (due on October 25th) Exercise 2 from the "Solving Logic Problems" (by G. Novak) handout (the Santa/Rudolph/Scrooge problem).

4. * (due on October 25th) Let p be a 4-ary relational symbol. Consider the following first order sentence:
" x [ \$ y [ " w [ \$ z [ p(x,y,w,z) ] ] ] ]

that is: forall x [ thereis y [ forall w [ thereis z p(x,y,w,z) ] ] ]

Show how to apply Skolemnization to this sentence to remove all its quantifiers. Explain your answer.