Transformation-Based Bottom-Up Computation of the Well-Founded Model

TL;DR

This paper introduces a transformation-based framework for efficiently computing the well-founded model of non-disjunctive logic programs, improving upon existing methods with polynomial complexity and confluence properties.

Contribution

It presents a novel transformation approach using conditional facts and strategies that unify and enhance known computational methods for the well-founded model.

Findings

Residual programs are polynomial in size for function-free programs.

Strategies correspond to known methods like the alternating fixpoint approach.

The method computes relevant parts of the well-founded model accurately and efficiently.

Abstract

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.