Default Logic and Bounded Treewidth

  • Johannes K. Fichte
  • Markus Hecher
  • Irina Schindler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10792)


In this paper, we study Reiter’s propositional default logic when the treewidth of a certain graph representation (semi-primal 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 (Ext). Our algorithm can even be used to enumerate all generating defaults (EnumSE) that lead to stable extensions. We show that our algorithm decides Ext in linear time in the input theory and triple exponential time in the treewidth (so-called fixed-parameter linear algorithm). Further, our algorithm solves EnumSE with a pre-computation step that is linear in the input theory and triple exponential in the treewidth followed by a linear delay to output solutions.


Parameterized algorithms Tree decompositions Dynamic programming Reiter’s default logic Propositional logic 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Technische Universität WienViennaAustria
  2. 2.Leibniz Universität HannoverHannoverGermany

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