## Artificial Intelligence: Problem Set 3

Assigned: Feb. 27
Due: Mar. 20

Consider a domain whose entities are people, books, and volumes.
(A "volume" is a particular physical object, which is a copy of an
abstract "book", like *Moby Dick*).

Let L be the first-order language containing the following predicates:

o(P,V) --- Predicate. Person P owns volume V

c(V,B) --- Predicate. Volume V is a copy of book B.

a(P,B) --- Predicate. Person P is the author of book B.

i(P,B) --- Predicate. Person P is the illustrator of book B.

h --- Constant. Howard Pyle.

s --- Constant. Sam.

j --- Constant. Joe.

### Problem 1

Express the following statements in L: (Note correction to sentence d.)
- a. Sam owns a copy of every book that Howard Pyle illustrated.
- b. Joe owns a copy of a book that Howard Pyle wrote.
- c. Howard Pyle illustrated every book that he wrote.
- d. Sam owns only illustrated books. Interpret this in the form
"If Sam owns volume V and V is a copy of book B, then B has been
illustrated by someone."
- e. None of the books that Joe has written have been illustrated by anyone.
- f. Sam does not own a copy of any book that Joe has written.
- g. There is a book
*B* such that both Sam and Joe own a copy of
*B*.

### Problem 2

Using resolution, show that (g) can be proven from (a-c) and that
(f) can be proven from (d,e). You must show the Skolemized form
of each of the axioms and of the negated goals. You need not show
the intermediate steps of Skolemization.