On the Power of Algebras with Recursion

We consider the relationship between the deductive and the functional/algebraic query language paradigms. Previous works considered this subject for a non-recursive algebra, or an algebra with a fixed point operation, and the corresponding class of deductive queries is that defined by stratified programs. We consider here algebraic languages extended by general recursive definitions. We also consider languages that allow non-restricted use of negation. It turns out that recursion and negation in the algebraic paradigm need to be studied together. The semantics used for the comparison is the valid semantics, although other well-known declarative semantics can also be used to derive similar results. We show that the class of queries expressed by general deduction with negation can be captured using algebra with recursive definitions.