Comparing Disjunctive Well-founded Semantics

While the stable model semantics, in the form of Answer Set Programming, has become a successful semantics for disjunctive logic programs, a corresponding satisfactory extension of the well-founded semantics to disjunctive programs remains to be found. The many current proposals for such an extension are so diverse, that even a systematic comparison between them is a challenging task. In order to aid the quest for suitable disjunctive well-founded semantics, we present a systematic approach to a comparison based on level mappings, a recently introduced framework for characterizing logic programming semantics, which was quite successfully used for comparing the major semantics for normal logic programs. We extend this framework to disjunctive logic programs, which will allow us to gain comparative insights into their different handling of negation. Additionally, we show some of the problems occurring when trying to handle minimal models (and thus disjunctive stable models) within the framework.