2. Consider the Datalog program P: T(x) + f(x), T(x) = a(x, y) A T(y) Ab(x, z) AT(2). (a) Describe, in your own words, the kind of structures that the query (T,P) recog- nises. [4 marks] (b) Compute the semi-naive evaluation of P for the database D with the following facts: e(1) e(2) e(6) a(3,1) a(4,3) a(5,3) a(7,5) b(3,2) b(5,3) b(7,6) Specify for each newly derived fact which of the rule(s) will produce it at the given point in the derivation. [5 marks] 2. Consider the Datalog program P: T(x) + f(x), T(x) = a(x, y) A T(y) Ab(x, z) AT(2). (a) Describe, in your own words, the kind of structures that the query (T,P) recog- nises. [4 marks] (b) Compute the semi-naive evaluation of P for the database D with the following facts: e(1) e(2) e(6) a(3,1) a(4,3) a(5,3) a(7,5) b(3,2) b(5,3) b(7,6) Specify for each newly derived fact which of the rule(s) will produce it at the given point in the derivation. [5 marks]