Why not negation by fixpoint?
Phokion G. Kolaitis, Christos H. Papadimitriou · 1988
There is a fixpoint semantics for DATALOG programs with negation that is a natural generalization of the standard semantics for DATALOG programs without negation. We show that, unfortunately, several compelling complexity-theoretic obstacles rule out its efficient implementation. As an alternative, we propose Inflationary DATALOG, an efficiently implementable semantics for negation, based on inflationary fixpoints