Semantics of Logic Programs: Their Intuitions and Formal Properties. An Overview

44 played a dominant role in Przymusinski's versions of WFS and ST N. The results of Section 4 underline the very strong relationship of NMR-semantics with nonmonotonic logics. We have also tried (in Section 5) to use another branch of nonmonotonic logics in order to get a classiication of the various diierent semantics: the approach, pioneered by Makinson, Kraus, Lehmann and Magidor, of inspecting abstract properties like Cumulativity and Rationality. In addition, we presented new principles, speciically tailored to be used in our framework of logic programs. This approach can be seen as an axiomatic framework and attempts to characterize the semantics uniquely by their abstract properties. It turned out that all these properties can also be used to reduce the computational complexity and compute a semantics more eeciently ((DM93c]). Acknowledgements Many thanks to Martin M uller who proofread parts of this paper and made a lot of helpful remarks during many talks. Discussions with Heinrich Herre and useful suggestions of John Schlipf, Roland Bol and Thomas Eiter also helped to improve this paper a lot. Roland Bol also suggested to consider k-maximal stable models and Michael Gelfond turned the author's attention to You and Yuan's work. E-mail discussions with Li-Yan Yuan, Jia-Huai You and Teodor Przymusinski helped to correct some hasty conjectures. Hans Rott noticed many typing errors.