The Complexity of Reasoning for Fragments of Autoepistemic Logic

Authors Nadia Creignou, Arne Meier, Michael Thomas, Heribert Vollmer

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Nadia Creignou
Arne Meier
Michael Thomas
Heribert Vollmer

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Nadia Creignou, Arne Meier, Michael Thomas, and Heribert Vollmer. The Complexity of Reasoning for Fragments of Autoepistemic Logic. In Circuits, Logic, and Games. Dagstuhl Seminar Proceedings, Volume 10061, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


Autoepistemic logic extends propositional logic by the modal operator L. A formula that is preceded by an L is said to be "believed". The logic was introduced by Moore 1985 for modeling an ideally rational agent's behavior and reasoning about his own beliefs. In this paper we analyze all Boolean fragments of autoepistemic logic with respect to the computational complexity of the three most common decision problems expansion existence, brave reasoning and cautious reasoning. As a second contribution we classify the computational complexity of counting the number of stable expansions of a given knowledge base. To the best of our knowledge this is the first paper analyzing the counting problem for autoepistemic logic.
  • Autoepistemic logic
  • computational complexity
  • nonmonotonic reasoning
  • Post's lattice


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