Consider a deductive database with the following rules:

ANCESTOR(X, Y) :– FATHER(X, Y)
ANCESTOR(X, Y) :– FATHER(X, Z), ANCESTOR(Z, Y)

Notice that FATHER(X, Y) means that Y is the father of X; ANCESTOR(X, Y) means that Y is the ancestor of X.

Consider the following fact base:

FATHER(Harry, Issac), FATHER(Issac, John), FATHER(John, Kurt)

a. Construct a model-theoretic interpretation of the above rules using the given facts.

b. Consider that a database contains the above relations FATHER(X, Y), another relation BROTHER(X, Y), and a third relation BIRTH(X, B), where B is the birth date of person X. State a rule that computes the first cousins of the following variety: their fathers must be brothers.

c. Show a complete Datalog program with fact-based and rule-based literals that computes the following relation: list of pairs of cousins, where the first person is born after 1960 and the second after 1970. You may use greater than as a built-in predicate.