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Proof Complexity of Propositional Default Logic

Authors: Olaf Beyersdorff, Arne Meier, Sebastian Müller, Michael Thomas, and Heribert Vollmer

Published in: Dagstuhl Seminar Proceedings, Volume 10061, Circuits, Logic, and Games (2010)

Abstract

Default logic is one of the most popular and successful formalisms for non-monotonic reasoning. In 2002, Bonatti and Olivetti introduced several sequent calculi for credulous and skeptical reasoning in propositional default logic. In this paper we examine these calculi from a proof-complexity perspective. In particular, we show that the calculus for credulous reasoning obeys almost the same bounds on the proof size as Gentzen's system LK. Hence proving lower bounds for credulous reasoning will be as hard as proving lower bounds for LK. On the other hand, we show an exponential lower bound to the proof size in Bonatti and Olivetti's enhanced calculus for skeptical default reasoning.

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Olaf Beyersdorff, Arne Meier, Sebastian Müller, Michael Thomas, and Heribert Vollmer. Proof Complexity of Propositional Default Logic. In Circuits, Logic, and Games. Dagstuhl Seminar Proceedings, Volume 10061, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{beyersdorff_et_al:DagSemProc.10061.5,
  author =	{Beyersdorff, Olaf and Meier, Arne and M\"{u}ller, Sebastian and Thomas, Michael and Vollmer, Heribert},
  title =	{{Proof Complexity of Propositional Default Logic}},
  booktitle =	{Circuits, Logic, and Games},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10061},
  editor =	{Benjamin Rossman and Thomas Schwentick and Denis Th\'{e}rien and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10061.5},
  URN =		{urn:nbn:de:0030-drops-25261},
  doi =		{10.4230/DagSemProc.10061.5},
  annote =	{Keywords: Proof complexity, default logic, sequent calculus}
}

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DOI: 10.4230/DagSemProc.10061.6

The Complexity of Reasoning for Fragments of Autoepistemic Logic

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

Published in: Dagstuhl Seminar Proceedings, Volume 10061, Circuits, Logic, and Games (2010)

Abstract

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.

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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)

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@InProceedings{creignou_et_al:DagSemProc.10061.6,
  author =	{Creignou, Nadia and Meier, Arne and Thomas, Michael and Vollmer, Heribert},
  title =	{{The Complexity of Reasoning for Fragments of Autoepistemic Logic}},
  booktitle =	{Circuits, Logic, and Games},
  pages =	{1--10},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10061},
  editor =	{Benjamin Rossman and Thomas Schwentick and Denis Th\'{e}rien and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10061.6},
  URN =		{urn:nbn:de:0030-drops-25234},
  doi =		{10.4230/DagSemProc.10061.6},
  annote =	{Keywords: Autoepistemic logic, computational complexity, nonmonotonic reasoning, Post's lattice}
}

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Documents authored by Thomas, Michael

Proof Complexity of Propositional Default Logic

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The Complexity of Reasoning for Fragments of Autoepistemic Logic

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