Use Resolution to answer the question, “What course would Steve like?

a) Steve only likes easy courses.
b) Science courses are hard.
c) All the courses in the basket weaving department are easy.
d) BK301 is a basket weaving course.

Use Resolution to answer the question, “What course would Steve like?

Solution ::

Steve would like BK301.

Step 1: Predicate logic (taking statement (a) in the usual textbook form, "Steve likes the courses that are easy"):

1. \(\forall x\ \text{easy}(x) \rightarrow \text{likes}(\text{steve}, x)\)
2. \(\forall x\ \text{science}(x) \rightarrow \neg\text{easy}(x)\)
3. \(\forall x\ \text{basketweaving}(x) \rightarrow \text{easy}(x)\)
4. \(\text{basketweaving}(\text{bk301})\)

Step 2: Clause form

1. \(\neg\text{easy}(x) \lor \text{likes}(\text{steve}, x)\)
2. \(\neg\text{science}(y) \lor \neg\text{easy}(y)\)
3. \(\neg\text{basketweaving}(z) \lor \text{easy}(z)\)
4. \(\text{basketweaving}(\text{bk301})\)

Step 3: Negate the question. "What course would Steve like?" is \(\exists w\ \text{likes}(\text{steve}, w)\). Its negation is the clause

5. \(\neg\text{likes}(\text{steve}, w)\)

Step 4: Resolution

¬likes(steve,w)      ¬easy(x) ∨ likes(steve,x)
          \          /   {x/w}
          ¬easy(w)       ¬basketweaving(z) ∨ easy(z)
               \         /   {z/w}
          ¬basketweaving(w)      basketweaving(bk301)
                    \            /   {w/bk301}
                         NIL

The empty clause (contradiction) is reached with the substitution \(w = \text{bk301}\). So the answer to the query is BK301. Clause 2 (science courses are hard) is not needed; it only tells us Steve would not like a science course.