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A ‘Theory’ Mechanism for a Proof-Verifier Based on First-Order Set Theory

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Computational Logic: Logic Programming and Beyond

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2408))

Abstract

We propose classical set theory as the core of an automated proof-verifier and outline a version of it, designed to assist in proof development, which is indefinitely expansible with function symbols generated by Skolemization and embodies a modularization mechanism named ‘theory’. Through several examples, centered on the finite summation operation, we illustrate the potential utility in large-scale proof-development of the ‘theory’ mechanism: utility which stems in part from the power of the underlying set theory and in part from Skolemization.

E.G. Omodeo enjoyed a Short-term mobility grant of the Italian National Research Council (CNR) enabling him to stay at the University of New York during the preparation of this work.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, University of L’Aquila, Italy

    Eugenio G. Omodeo

  2. Department of Computer Science, Courant Institute of Mathematical Sciences, University of New York, USA

    Jacob T. Schwartz

Authors
  1. Eugenio G. Omodeo
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  2. Jacob T. Schwartz
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Cyprus, 75 Kallipoleos St., 1678, Nicosia, Cyprus

    Antonis C. Kakas

  2. Department of Computing, Imperial College of Science, Technology and Medicine, 180 Queen’s Gate, London, SW7 2BZ, UK

    Fariba Sadri

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© 2002 Springer-Verlag Berlin Heidelberg

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Omodeo, E.G., Schwartz, J.T. (2002). A ‘Theory’ Mechanism for a Proof-Verifier Based on First-Order Set Theory. In: Kakas, A.C., Sadri, F. (eds) Computational Logic: Logic Programming and Beyond. Lecture Notes in Computer Science(), vol 2408. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45632-5_9

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  • DOI: https://doi.org/10.1007/3-540-45632-5_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43960-8

  • Online ISBN: 978-3-540-45632-2

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