D-wfs: a Connuent Calculus and an Equivalent Characterization

Quite recently Brass/Dix have introduced the semantics D-WFS based on an abstract framework and the notion of Partial Evaluation. Besides the abstract deenition, D-WFS can also be seen as a proof-theoretic attempt, associating to any program a normalform ^ , called the residual program. We show in this paper, that our original calculus consisting of some simple transformations is in fact connuent, i.e. all transformations can be applied in any order: if we arrive at an irreducible program (no more transformation is applicable) then this is already the unique normalform. We also give an equivalent characterization of D-WFS in terms of iterated minimal model reasoning. Our construction is a generalization of a description of the wellfounded semantics: we introduce a very simple and neat construction of a sequence D i that eventually stops and represents the set of derivable disjunctions.