Exercise 12.3 Consider the following knowledge base:

r(a).

r(e).

p(c).

q(b).

s

(a, b).

s

(d, b).

s

(e, d).

p(X) ← q(X) ∧ r(X).

q(X) ← s(X, Y) ∧ q(Y).

Show the set of ground atomic consequences derivable from this knowledge base.

Assume that a bottom-up proof procedure is used and that at each iteration the first applicable clause is selected in the order shown. Furthermore, applicable constant substitutions are chosen in “alphabetic order” if more than one applies to a given clause; for example, if X/a and X/b are both applicable for a clause at some iteration, derive q

(a) first. In what order are consequences derived?