Bottom-up evaluation of datalog with negation

Declarative semantics gives the meaning of a logic program in terms of properties, while the procedural semantics gives the meaning in terms of the execution or evaluation of the program. From the database point of view, the procedural semantics of the program is equally important. This paper focuses on the study of the bottom-up evaluation of the WFM semantics of datalog ^- programs. To compute the WFM, first, the stability transformation is revisited, and a new operator O _P and its fixpoint are defined. Based on this, a fixpoint semantics, called oscillating fixpoint model semantics, is defined. Then, it is shown that for any datalog ^- program the oscillating fixpoint model is identical to its WFM. So, the oscillating fixpoint model can be viewed as an alternative (constructive) definition of WFM. The underlying operation (or transformation) for reaching the oscillating fixpoint provides a potential of bottom-up evaluation. For the sake of computational feasibility, the strongly range-restricted program is considered, and an algorithm used to compute the oscillating fixpoint is described.