AI: Problem Set 3

Assigned: Feb. 19
Due: March 2

Problem 1

Let D be the domain of solid objects. Let L be the first-order language over D with the following non-logical symbols:
inside(O1,O2) --- Object O is inside O2.
empty(O) --- Object O is empty.
accessible(O) --- Object O is accessible.
red(O) --- Object O is red.
Represent the following statements in L.

Problem 2

Convert sentences A through E above, and the negations of sentences F and G to clausal form (CNF).

Problem 3

Give resolution proofs of F and G from A-E. (No credit will be given for a proof that is not a resolution proof.)

Proof of F

H. inside(sk1(sk4),sk4).  From [not F].2 and A.2, O1 -> sk4.
I. ~accessible(sk1(sk4)). From H and B.1, O1 -> sk1(sk4), O2 -> sk4
J. empty clause.          From I and [not F].1, O -> sk1(sk4).

Proof of G

K. ~accessible(sk5).      From [not G] and D. O -> sk5
L. accessible(sk3(sk5)).  From K and C.1. O -> sk5.
M. inside(sk5,sk3(sk5)).  From K and C.2, O -> sk5.
N. red(sk3(sk5)).         From L and D.   O -> sk3(sk5).
P. ~red(sk3(sk5)) V red(sk5). From M and E, O1 -> sk5, O2 -> sk3(sk5).
Q. red(sk5).              From P and N.
R. empty                  From Q and [not G].