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A Better Logical Semantics for Prolog

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Prolog: The Next 50 Years

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13900))

Abstract

This paper describes a semantics for the language of pure positive Prolog programs that improves on the widely accepted Least Herbrand Model (LHM) semantics. The LHM semantics gives meaning only to complete Prolog programs, and not to components of programs. Yet programmers clearly understand the meaning of a predicate even if not all predicates used in its definition are defined in the program. For example, programmers understand the meaning of the two rules defining transitive closure without having to know the specific graph that it applies to. A semantics for the Prolog language should also provide such a meaning. We motivate the meaning of Prolog rules as inductive definitions by starting with Clark’s completion, analyzing its limitations, and then describing how it can be modified to yield a logical theory of inductive definitions.

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Notes

  1. 1.

    Also available at: https://people.cs.kuleuven.be/~marc.denecker/A-PDF/Prolog50.pdf.

  2. 2.

    The form of the not operator in most Prologs is \(\mathtt{\backslash +}\), which is intended to approximate in ASCII the logical proves symbol \(\vdash \) with a slash / through it.

  3. 3.

    See a footnote in [6] for a proof.

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Author information

Authors and Affiliations

  1. Stony Brook University, New York, UK

    David S. Warren

  2. KU Leuven, Leuven, Belgium

    Marc Denecker

Authors
  1. David S. Warren
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  2. Marc Denecker
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Correspondence to David S. Warren .

Editor information

Editors and Affiliations

  1. Stony Brook University, Stony Brook, NY, USA

    David S. Warren

  2. Simon Fraser University, Burnaby, BC, Canada

    Veronica Dahl

  3. TU Wien, Vienna, Austria

    Thomas Eiter

  4. Universidad Politecnica de Madrid/IMDEA Software Institute, Madrid, Spain

    Manuel V. Hermenegildo

  5. Imperial College London, London, UK

    Robert Kowalski

  6. IBM Research, Yorktown Heights, NY, USA

    Francesca Rossi

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Warren, D.S., Denecker, M. (2023). A Better Logical Semantics for Prolog. In: Warren, D.S., Dahl, V., Eiter, T., Hermenegildo, M.V., Kowalski, R., Rossi, F. (eds) Prolog: The Next 50 Years. Lecture Notes in Computer Science(), vol 13900. Springer, Cham. https://doi.org/10.1007/978-3-031-35254-6_7

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  • DOI: https://doi.org/10.1007/978-3-031-35254-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-35253-9

  • Online ISBN: 978-3-031-35254-6

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