## Problem Set 2

Assigned: Sept. 17
Due: Sept. 24

Let U be a universe containing the following kinds of entities:

• People.
• Books, in the abstract sense. E.g. "War and Peace" is a book.
• Volumes, in the concrete sense. A volume is a one particular object made of paper, ink, etc.

Let L be the first-order language containing the following primitives

• owns(P,V) --- Predicate. Person P owns volume V.
• wrote(P,B) --- Predicate. Person P wrote book B. (Note: A book may have several authors.)
• copy(V,B) --- Predicate. Volume V is a copy of book B.
• russell, norvig, tolstoy, becky, chris--- Constants denoting people.
• aima, wp, ak -- Constants denoting the books "AI: A Modern Approach", "War and Peace", and "Anna Karenina" respectively.
Express the following statements in L:
• 1. Tolstoy wrote both "War and Peace" and "Anna Karenina".
• 2. Russell and Norvig wrote "AI: A Modern Approach".
• 3. There are no books that were jointly written by Tolstoy and by Russell.
• 4. There is a book that was written by Norvig but not by Russell.
• 5. Chris owns a copy of "War and Peace".
• 6. Becky owns a copy of every book that Tolstoy wrote.
• 7. Chris does not own any copy of "AI: A Modern Approach".
• 8. All the volumes that Chris owns are copies of books written by Tolstoy.
• 9. There is a book B by Russell such that Becky owns a copy of B but Chris does not own a copy of B.
• 10. Becky owns a copy of every book written by Tolstoy.
• 11. Russell owns a copy of every book that he himself has written.
• 12. Becky wrote a book, but no copies of the book exist.