Default Logic and Bounded Treewidth

06/28/2017

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by   Johannes K. Fichte, et al.

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In this paper, we study Reiter's propositional default logic when the treewidth of a certain graph representation (semi-incidence graph) of the input theory is bounded. We establish a dynamic programming algorithm on tree decompositions that decides whether a theory has a consistent stable extension or can even be used to enumerate all generating defaults that lead to stable extensions. We show that, for input theories whose semi-incidence graph has bounded treewidth, our algorithm decides whether a theory has a stable extension in linear time and enumerates all characteristic generating defaults with linear delay.