Focusing in linear meta-logic: extended report

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 {\em 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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https://hal.inria.fr/inria-00281631
Contributor : Vivek Nigam <>
Submitted on : Saturday, May 24, 2008 - 11:06:58 AM
Last modification on : Wednesday, March 27, 2019 - 4:41:26 PM
Long-term archiving on: Friday, May 28, 2010 - 7:59:44 PM

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Vivek Nigam, Dale Miller. Focusing in linear meta-logic: extended report. [Research Report] Maybe this file need a better style. Specially the proofs., 2008. ⟨inria-00281631⟩

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