6. [10%] Resolution Proof
Consider the following problem:
There are 2 students, S1, S2. They are
students of a program with multiple
classes (C1, C2, C3, C4) that belong
to 2 different class groups (G1, G2):
1. C1 and C2 are in group G1.
2. C3 and C4 are in group G2.
A student in the school must satisfy the following requirements to graduate:
3. The student must pass at least one course in each class group to pass that class group.
4. The student must pass G1 and G2 with the same fellow student.
5. The student must pass C1.
We now have the following facts about the students:
6. S1 passes C1.
7. S1 passes C2.
8. S1 doesn't pass C3.
9. S1 passes C4.
10.S2 passes C1.
11.S2 passes C2.
12. S2 passes C3.
6A. [10%] Create the knowledge base and answer the query: "Can S1 graduate?" using a
refutation proof with resolution. Indicate all substitutions used.
NOTE: You do not need to use Student(x) or Class(x) to indicate that x is a student or a class. E.g.,
you can translate statement 1 into "IG(C1, G1) ^ IG(C2, G1)". Hint: When you turn statement 4 to a
KB sentence, you can directly use S2 for "there exists student y" (since this problem only considers
two students, S1 and S2).
Use only the following predicates:
\begin{itemize}
\item P(x, y): student x passes class y.
\item G(x): x can graduate.
\item PG(x, y): x passes class group y.
\item IG(x, y): class x is in group y.
\end{itemize}
