Translate the statements A1 through A4 into clausal form. Show that the predicate supports(book,cup) is true using resolution.

Let us look at the question first. The question is:

Given the following information for a database

• A1. If x is on top of y, y supports x.

• A2. If x is above y and they are touching each other, x is on top of y.

• A3. A cup is above a book.

• A4. A cup is touching a book.
  

(i) Translate the statements A1 through A4 into clausal form.

(ii) Show that the predicate supports(book, cup) is true using resolution.

Let us first convert A1 into clausal form.

top(x,y) ⟹ supports(y,x)

Now, let us convert A2.

above(x,y) & (touch(x,y) ∨ touch(y,x)) ⟹ top(x,y)

Now let us convert A3.

above(cup,book)

Let us now convert A4.

touch(book,cup)

Now, applying conjunction (AND) on statements A3 and A4, we get.

above(cup,book) & touch(book,cup) ⟹ top(cup,book)

Now, from this statement and A1, we get

top(cup,book) ⟹ supports(book,cup)