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On resolution in fragments of classical linear logic (extended abstract)

  • Session 2: Non-Resolution Theorem Proving I
  • Conference paper
  • First Online:
Logic Programming and Automated Reasoning (LPAR 1992)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 624))

Abstract

We present a proof-theoretic foundation for logic programming in Girard's linear logic. We exploit the permutability properties of two-sided linear sequent calculus to identify appropriate notions of uniform proof, definite formula, goal formula, clause and resolution proof for fragments of linear logic. The analysis of this paper extends earlier work by the present authors to include $negative occurrences of ✠ (par) and positive occurrences of ! (of course !) and ? (why not ?). These connectives introduce considerable difficulty. We consider briefly some of the issues related to the mechanical implementation of our resolution proofs.

Supported by a grant of the Australian Research Council through the Machine Intelligence Project.

Supported by U.K. Science and Engineering Research Council grant GR/G 58588, “Logical and Semantical Frameworks”.

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Author information

Authors and Affiliations

  1. University of Melbourne, Australia

    J. A. Harland

  2. University of Edinburgh, Scotland, UK

    D. J. Pym

Authors
  1. J. A. Harland
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  2. D. J. Pym
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Editor information

Andrei Voronkov

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© 1992 Springer-Verlag Berlin Heidelberg

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Harland, J.A., Pym, D.J. (1992). On resolution in fragments of classical linear logic (extended abstract). In: Voronkov, A. (eds) Logic Programming and Automated Reasoning. LPAR 1992. Lecture Notes in Computer Science, vol 624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013046

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  • DOI: https://doi.org/10.1007/BFb0013046

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55727-2

  • Online ISBN: 978-3-540-47279-7

  • eBook Packages: Springer Book Archive

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