1.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?
2. Consider the following knowledge base:
has_access(X,library) ←student(X).
has_access(X,library) ←faculty(X).
has_access(X,library) ←has_access(Y,library) ∧parent(Y,X).
has_access(X,office) ←has_keys(X).
faculty(diane).
faculty(ming).
student(william).
student(mary).
parent(diane,karen).
parent(diane,robyn).
parent(susan,sarah).
parent(sarah,ariel).
parent(karen,mary).
parent(karen,todd).
a. Provide an SLD derivation of the query ask has_access(todd,library).
b. The query ask has_access(mary,library) has two SLD derivations. Give both of them.
c. Does there exist an SLD derivation for ask has_access(ariel,library)? Explain why or why not.
d. Explain why the set of answers to the query ask has_access(X,office) is empty.
e. Suppose following the clause is added to the knowledge base:
has_keys(X) ←faculty(X).
What are the answers to the query ask has_access(X,office)