A Comparative Study of Disjunctive Well-Founded Semantics

A lot of different proposals were made claiming to extend the wellfounded semantics to logic programs with disjunction. None of these however has been established as ’the’ disjunctive well-founded semantics which is mainly caused by the different intuitive ideas on which these semantics are based. In fact, some of them are even incomparable with respect to their derivable knowledge, and systematic comparisons are rather rarely done. A recently introduced framework for characterizing logic programming semantics was quite successfully used for comparing the major semantics for normal logic programs. We are going to extend this framework to disjunctive logic programs and will present alternative characterizations for three semantics for disjunctive logic programs, namely the strong well-founded semantics (SWFS), the generalized disjunctive well-founded semantics (GDWFS), and the disjunctive well-founded semantics (D-WFS). We will see that this cannot be done in a straightforward way. Whereas the derivation of positive information is more or less uniform, obtained negative information differs and some of the constructions even show the limits of the applied framework. We will also mention the difficulties when characterizing two major two-valued semantics for disjunctive logic programs, minimal models and disjunctive stable models. Acknowledgment This work has been supported by the German Academic Exchange Service (DAAD) and by the ’Gesellschaft von Freunden und Förderern der Technischen Universität Dresden e.V.’.