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Focusing in Linear Meta-logic

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Automated Reasoning (IJCAR 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5195))

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Abstract

It is well known how to use an intuitionistic meta-logic to specify natural deduction systems. It is also possible to use linear logic as a meta-logic for the specification of a variety of sequent calculus proof systems. Here, we show that if we adopt different focusing annotations for such linear logic specifications, a range of other proof systems can also be specified. In particular, we show that natural deduction (normal and non-normal), sequent proofs (with and without cut), tableaux, and proof systems using general elimination and general introduction rules can all be derived from essentially the same linear logic specification by altering focusing annotations. By using elementary linear logic equivalences and the completeness of focused proofs, we are able to derive new and modular proofs of the soundness and completeness of these various proofs systems for intuitionistic and classical logics.

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Authors and Affiliations

  1. INRIA & LIX/École Polytechnique, Palaiseau, France

    Vivek Nigam & Dale Miller

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  1. Vivek Nigam
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  2. Dale Miller
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Alessandro Armando Peter Baumgartner Gilles Dowek

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Nigam, V., Miller, D. (2008). Focusing in Linear Meta-logic. In: Armando, A., Baumgartner, P., Dowek, G. (eds) Automated Reasoning. IJCAR 2008. Lecture Notes in Computer Science(), vol 5195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71070-7_42

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  • DOI: https://doi.org/10.1007/978-3-540-71070-7_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71069-1

  • Online ISBN: 978-3-540-71070-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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