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The complexity of reasoning for fragments of default logic

Beyersdorff, O, Meier, A, Thomas, M and Vollmer, H (2012) The complexity of reasoning for fragments of default logic. Journal of Logic and Computation, 22 (3). 587 - 604 . ISSN 0955-792X

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Abstract

Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as Σ -complete, and the complexity of the credulous and skeptical reasoning problem as Σ -complete, respectively Π -complete. Additionally, he investigated restrictions on the default rules, i.e. semi-normal default rules. Selman used in 1992 a similar approach with disjunction-free and unary default rules. In this article, we systematically restrict the set of allowed propositional connectives. We give a complete complexity classification for all sets of Boolean functions in the meaning of Post's lattice for all three common decision problems for propositional default logic. We show that the complexity is a hexachotomy (Σ -, Δ -, NP-, P-, NL-complete, trivial) for the extension existence problem, while for the credulous and skeptical reasoning problem we obtain similar classifications without trivial cases.

Item Type: Article
Copyright, Publisher and Additional Information: © 2012, Oxford University Press. This is an author produced version of a paper published in Journal of Logic & Computation. Uploaded in accordance with the publisher's self-archiving policy.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 18 Jul 2012 12:41
Last Modified: 08 Feb 2013 17:39
Published Version: http://dx.doi.org/10.1093/logcom/exq061
Status: Published
Publisher: Oxford University Press
Identification Number: 10.1093/logcom/exq061
URI: http://eprints.whiterose.ac.uk/id/eprint/74431

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