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Elimination of Negation in a Logical Framework

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Computer Science Logic (CSL 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1862))

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Abstract

Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF) [12] cannot express directly negative information, although negation is a useful specification tool. Since negation-as-failure does not fit well in a logical framework, especially one endowed with hypothetical and parametric judgments, we adapt the idea of elimination of negation introduced in [17] for Horn logic to a fragment of higher-order HHF. This entails finding a middle ground between the Closed World Assumption usually associated with negation and the Open World Assumption typical of logical frameworks; the main technical idea is to isolate a set of programs where static and dynamic clauses do not overlap.

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Author information

Authors and Affiliations

  1. Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Alberto Momigliano

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  1. Alberto Momigliano
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Department of Biology, Boston College, Fulton Hall 410B, Chestnut Hill, MA, 02467, USA

    Peter G. Clote

  2. Mathematisches Institut, Ludwig-Maximilian-Universität München, Theresienstr. 39, 80333, München, Germany

    Helmut Schwichtenberg

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© 2000 Springer-Verlag Berlin Heidelberg

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Momigliano, A. (2000). Elimination of Negation in a Logical Framework. In: Clote, P.G., Schwichtenberg, H. (eds) Computer Science Logic. CSL 2000. Lecture Notes in Computer Science, vol 1862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44622-2_28

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  • DOI: https://doi.org/10.1007/3-540-44622-2_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67895-3

  • Online ISBN: 978-3-540-44622-4

  • eBook Packages: Springer Book Archive

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