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Logic for Programming, Artificial Intelligence, and Reasoning

LPAR 2015: Logic for Programming, Artificial Intelligence, and Reasoning pp 402–417Cite as

A Contextual Logical Framework

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9450))

Abstract

A new logical framework with explicit linear contexts and names is presented with the purpose of enabling direct and flexible manipulation of contexts, both for representing systems and meta-properties. The framework is a conservative extension of the logical framework LF, and builds on linear logic and contextual modal type theory. We prove that the framework admits canonical forms, and that it possesses all desirable meta-theoretic properties, in particular hereditary substitutions.

As proof of concept, we give an encoding of the one-sided sequent calculus for classical linear logic and the corresponding cut-admissibility proof, as well as an encoding of parallel reduction of lambda terms with the corresponding value-soundness proof.

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Notes

  1. 1.

    This is the same restriction as in traditional CMTT for LF, since it would lead to commuting conversions.

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Acknowledgments

We would like to thank Daniel Gustafsson for invaluable feedback. This work is funded by the DemTech grant 10-092309 of the Danish Council for Strategic Research on Democratic Technologies.

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Authors and Affiliations

  1. IT University of Copenhagen, Copenhagen, Denmark

    Peter Brottveit Bock & Carsten Schürmann

Authors
  1. Peter Brottveit Bock
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  2. Carsten Schürmann
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Corresponding author

Correspondence to Peter Brottveit Bock .

Editor information

Editors and Affiliations

  1. New York University, New York, New York, USA

    Martin Davis

  2. University of the South Pacific, Suva, Fiji

    Ansgar Fehnker

  3. Macquarie University, Sydney, New South Wales, Australia

    Annabelle McIver

  4. The University of Manchester, Manchester, United Kingdom

    Andrei Voronkov

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Bock, P.B., Schürmann, C. (2015). A Contextual Logical Framework. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2015. Lecture Notes in Computer Science(), vol 9450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48899-7_28

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  • DOI: https://doi.org/10.1007/978-3-662-48899-7_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48898-0

  • Online ISBN: 978-3-662-48899-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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