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Higher-Order Quantification and Proof Search*

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Book cover Algebraic Methodology and Software Technology (AMAST 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2422))

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Abstract

Logical equivalence between logic programs that are firstorder logic formulas holds between few logic programs, partly because first-order logic does not allow auxiliary programs and data structures to be hidden. As a result of not having such abstractions, logical equivalence will force these auxiliaries to be present in any equivalence program. Higher-order quantification can be use to hide predicates and function symbols. If such higher-order quantification is restricted so that operationally, only hiding is specified, then the cost of such higher-order quantifiers within proof search can be small: one only needs to deal with adding new eigenvariables and clauses involving such eigenvariables. On the other hand, the specification of hiding via quantification can allow for novel and interesting proofs of logical equivalence between programs. This paper will present several example of how reasoning directly on a logic program can benefit significantly if higher-order quantification is used to provide abstractions.

This work was supported in part by NSF grants CCR-9912387, CCR-9803971, INT- 9815645, and INT-9815731 and a one month guest professorship at L’Institut de Mathématiques de Luminy, University Aix-Marseille 2 in February 2002.

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Authors and Affiliations

  1. Computer Science and Engineering, 220 Pond Lab, Pennsylvania State University, University Park, 16802-6106, PA, USA

    Dale Miller

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  1. Dale Miller
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Editors and Affiliations

  1. LORIA - CNRS & INRIA, Campus Scientifique, Bâtiment LORIA, BP 239, 54506, Vandoeuvre-lès-Nancy, France

    Hélène Kirchner

  2. LORIA - INRIA, 615, rue du Jardin Botanique, 54602, Villers-lès-Nancy, France

    Christophe Ringeissen

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© 2002 Springer-Verlag Berlin Heidelberg

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Miller, D. (2002). Higher-Order Quantification and Proof Search* . In: Kirchner, H., Ringeissen, C. (eds) Algebraic Methodology and Software Technology. AMAST 2002. Lecture Notes in Computer Science, vol 2422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45719-4_5

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  • DOI: https://doi.org/10.1007/3-540-45719-4_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44144-1

  • Online ISBN: 978-3-540-45719-0

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