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Proof complexity of propositional default logic

Beyersdorff, O, Meier, A, Mueller, S, Thomas, M and Vollmer, H (2011) Proof complexity of propositional default logic. Archive for Mathematical Logic, 50 (7-8). 727 - 742 . ISSN 1432-0665

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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.

Item Type: Article
Copyright, Publisher and Additional Information: © 2011, Springer. This is an author produced version of a paper published in Archive for mathematical logic. Uploaded in accordance with the publisher's self-archiving policy. The original publication is available at www.springerlink.com
Keywords: Default logic, Sequent calculus, Proof complexity
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: 14 Jun 2012 14:20
Last Modified: 05 Jun 2014 17:45
Published Version: http://dx.doi.org/10.1007/s00153-011-0245-8
Status: Published
Publisher: Springer Verlag
Identification Number: 10.1007/s00153-011-0245-8
URI: http://eprints.whiterose.ac.uk/id/eprint/43919

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