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On intuitionistic query answering in description bases

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Book cover Automated Deduction — CADE-12 (CADE 1994)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 814))

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Abstract

In this paper we present a weak and a strong intuitionistic calculus for query answering in Description Logics (DL). Given the standard model-theoretic semantics for DL, a complete query-answering calculus has to perform complex case analyses to cope with implicit disjunctions stemming from some of the concept-forming operators in DL. To avoid this complexity we propose an intuitionistic approach to query answering based on the Sequent-Calculus-style axiomatization of DL we have developed in [20] and [21]. By taking into account only the intuitionistic inference schemata of this axiomatization, we obtain a strong intuitionistic query-answering calculus. An additional restriction to reasoning about explicit objects allows a further simplification of the proof theory and yields a weak intuitionistic calculus.

We prove completeness of these calculi wrt axiomatic semantics based on the Intuitionistic Sequent Calculus. For the weak calculus we also give a least fixed point semantics as known from Deductive Databases and Logic Programming.

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Authors and Affiliations

  1. ONERA DES/SIA, Avenue de la division Leclerc, B.P. 72, F-92322, Chatillon Cedex

    Véronique Royer

  2. Technische Universität Berlin, KIT-VM11, FR 5-12, Franklinstr. 28/29, D-10587, Berlin

    J. Joachim Quantz

Authors
  1. Véronique Royer
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  2. J. Joachim Quantz
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Alan Bundy

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© 1994 Springer-Verlag Berlin Heidelberg

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Royer, V., Quantz, J.J. (1994). On intuitionistic query answering in description bases. In: Bundy, A. (eds) Automated Deduction — CADE-12. CADE 1994. Lecture Notes in Computer Science, vol 814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58156-1_23

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  • DOI: https://doi.org/10.1007/3-540-58156-1_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58156-7

  • Online ISBN: 978-3-540-48467-7

  • eBook Packages: Springer Book Archive

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