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Minimal negation and Hereditary Harrop formulae

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Logical Foundations of Computer Science — Tver '92 (LFCS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 620))

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Abstract

Following an underrated paper by Miller [7], minimal negation is added to first-order Hereditary Harrop-formulae (fohh) at no computational cost, preserving their nature of abstract logic programming language [8]. The soundness and completeness theorem is proved with respect to natural deduction. The following relation with negation-as-failure holds: G has a SLDNF derivation from P iff G has a uniform proof from the completion of P. Moreover we show how to embed minimal, intuitionistic and classical logic into fohh: as a consequence and application of the two last results, the logic is shown to represent every partial recursive functions.

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Authors and Affiliations

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

    Alberto Momigliano

Authors
  1. Alberto Momigliano
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Anil Nerode Mikhail Taitslin

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© 1992 Springer-Verlag Berlin Heidelberg

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Momigliano, A. (1992). Minimal negation and Hereditary Harrop formulae. In: Nerode, A., Taitslin, M. (eds) Logical Foundations of Computer Science — Tver '92. LFCS 1992. Lecture Notes in Computer Science, vol 620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023886

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  • DOI: https://doi.org/10.1007/BFb0023886

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55707-4

  • Online ISBN: 978-3-540-47276-6

  • eBook Packages: Springer Book Archive

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