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On Proof Complexity of Circumscription

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1397))

Abstract

Circumscription is a non-monotonic formalism based on the idea that objects satisfying a certain predicate expression are considered as the only objects satisfying it. Theoretical complexity results imply that circumscription is (in the worst case) computationally harder than classical logic. This somehow contradicts our intuition about common- sense reasoning: non-monotonic rules should help to speed up the reasoning process, and not to slow it down.

In this paper, we consider a first-order sequent calculus for circumscription and show that the presence of circumscription rules can tremendously simplify the search for proofs. In particular, we show that certain sequents have only long “classical” proofs, but short proofs can be obtained by using circumscription.

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Author information

Authors and Affiliations

  1. Abt. Wissensbasierte Systeme 184/3, Technische Universität Wien, Treitlstraße 3, A-1040, Wien, Austria

    Uwe Egly & Hans Tompits

Authors
  1. Uwe Egly
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  2. Hans Tompits
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Editor information

Editors and Affiliations

  1. Faculty of Philosophy, Tilburg University, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands

    Harrie de Swart

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© 1998 Springer-Verlag Berlin Heidelberg

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Egly, U., Tompits, H. (1998). On Proof Complexity of Circumscription. In: de Swart, H. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 1998. Lecture Notes in Computer Science(), vol 1397. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69778-0_19

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  • DOI: https://doi.org/10.1007/3-540-69778-0_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64406-4

  • Online ISBN: 978-3-540-69778-7

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