CSE571 Class Notes for Sept. 17 Geoff Beerbower
Problem: Refuse admission to an applicant if he/she has not taken any honors course.
refuse_admission(X).
applicant(X).
taken_honors_course(X,Y).
refuse_admission(X) ← applicant(X), not taken_honors_course(X,Y).
applicant (john).
applicant (george).
taken_honors_course(john, chemistry).
taken_honors_course(george, physics).
Side Note: If we go by mathematical semantics, variables can go anywhere, so there would be
many instantiations. However, in “smodels” there is implicit typing. So in this example,
chemistry and physics can only appear in the Y position in the
“taken_honors_course(X,Y).” rule.
The above rules lead to the following instantiations:
1) refuse_admission(john) ← applicant(john), not
taken_honors_course(john, physics).
2) refuse_admission(john) ← applicant(john), not
taken_honors_course(john, chemistry).
3) refuse_admission(george) ← applicant(george), not
taken_honors_course(george, physics).
4) refuse_admission(george) ← applicant(george), not
taken_honors_course(george, chemistry).
Remember, the head of a rule is true if there is some combination of variables that make the
body true. Here, instantiation 2 causes john to be refused, even though he has taken an honors
course. Likewise, instantiation 4 causes george to be refused. The point is:
When using variables and not, be very careful what not means.
Solution: replace the first rule:
refuse_admission(X) ← applicant(X), not taken_honors_course(X,Y).
with the following two rules:
taken_honors_course(X)← taken_honors_course(X,Y).
refuse_admission(X) ← applicant(X), not taken_honors_course(X).
Side Note: If the original problem had been “Refuse admission to an applicant if he/she has not
taken all honors courses”, then the original solution would have been correct.
