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Classes C1 and C2 are hard to solve using SQL and the Relational Model. Datalog which offers Logic as the Data Model is capable of solving C1 (partially). It is done by introducing recursive rules which can be applied to cyclic data, but there will be problems with storing and presenting a solution.
Prolog is capable of handling both C1 and C2. It is done by introducing non atomic arguments together with rule recursiveness. Common solutions to problems of class C1 or C2 are given in [4,1]. Some examples are also presented in Chapter 12.