Question: 7. 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) .

7. 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 has_access(todd, library).

(b) The query has_access(mary, library) has two SLD derivations. Give both of them.

(c) Does there exist an SLD derivation for has_access(ariel, library)? Explain why or why not.

(d) Explain why the set of answers to the query has_access(X, office) is empty.

(e) Suppose the following clause is added to the knowledge base:

has_keys(X) ← faculty(X) .

What are the answers to the query has_access(X, office)?

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