Embedding deductive capabilities in relational database systems

The basic idea of our work is to include deductive capabilities in a relational database system by fully using the operands of relational algebra and without using any theorem prover. We present a deductive database system where the user can formulate deduction laws as logical formulas, but which works on an underlying relational database system by fully using the data manipulation routines of such a system. Generally, it is not possible to express the deduction laws by means of expressions of relational algebra (see Ref. 1). In our system, a relational algebra expression is associated with every database deduction law. The result of its evaluation (with respect to an underlying database) is the set of all database entries that can be deduced from the database by applying the respective law once (Theorem 1). By successively applying all these relational expressions for all the database deduction laws it is possible to generate the whole extensional database (i.e. all tuples deducible from the database).