Ordering default theories and nonmonotonic logic programs
A default theory contains different portions of information: classical/persistent and default/ten\-ta\-tive. These different portions are used in the paper to order default theories. The default theories are characterised by means of a bilattice-based many-valued interpretation having two orderings: information content ordering and truth ordering. When \(Th_1\leq_{DL} Th_2\), conclusions derived from \(Th_1\) are relatively less certain than those derived from \(Th_2\). Such an order \(\leq_{DL}\) is nonmonotonic w.r.t. the increase of information. This allows the author to study ordering relations in the answer-set semantics for nonmonotonic logic programs having many-valued interpretations (for this topic see also the influential paper by \textit{M. Gelfond} and \textit{V. Lifschitz} [New Gener. Comput. 9, No. 3/4, 365--385 (1991; Zbl 0735.68012)]).
scientific article; zbMATH DE number 2184037