AI: Problem Set 3
Assigned: Feb. 16
Due: Mar. 2
Let L be the following first-order language, over a universe of people
(that is, all terms refer to people):
c(X,Y) --- X is a child of Y.
g(X,Y) --- X is a grandchild of Y.
s(X,Y) --- X is a sibling of Y. (This includes half-siblings; also, a person
is considered his own sibling.)
r(X) --- X is in room 400.
e -- Constant: Ed.
Represent the following statements in L.
- A. X is a sibling of Y if and only if
there exists Z such that both X and Y are children of Z.
- B. X is a grandchild of Y if and only if there exists Z such that
X is a child of Z and Z is a child of Y.
- C. Everyone is the child of someone.
- D. If X is a sibling of Y, then there exists Z such that both
X and Y are grandchildren of Z.
- E. Everyone in room 400 is a child of Ed.
- F. Any two people in room 400 are siblings.
Give a resolution proof of D from A, B, and C. Please note:
- You need not show the intermediate stages of Skolemization. You must
show all the clauses generated. You must show all the resolutions.
- No credit will be given for a proof that is not a resolution proof.
Give a resolution proof of F from A and E.