We present a framework for expressing bottom-up algorithms to compute the
well-founded model of non-disjunctive logic programs. Our method is based on
the notion of conditional facts and elementary program transformations studied
by Brass and Dix for disjunctive programs. However, even if we restrict their
framework to nondisjunctive programs, their residual program can grow to
exponential size, whereas for function-free programs our program remainder is
always polynomial in the size of the extensional database (EDB).
We show that particular orderings of our transformations (we call them
strategies) correspond to well-known computational methods like the alternating
fixpoint approach, the well-founded magic sets method and the magic alternating
fixpoint procedure. However, due to the confluence of our calculi, we come up
with computations of the well-founded model that are provably better than these
methods.
In contrast to other approaches, our transformation method treats magic set
transformed programs correctly, i.e. it always computes a relevant part of the
well-founded model of the original program.Comment: 43 pages, 3 figure
