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inria-00281631, version 1

Focusing in linear meta-logic: extended report

Vivek Nigam () 1, Dale Miller 1

N° Maybe this file need a better style. Specially the proofs. (2008)

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.

  • Domain : Computer Science/Logic in Computer Science
  • Keywords : Proof Theory – Meta Logic – Focusing – Sequent Calculus – Natural Deduction – Free Deduction – General Elimination Rules – Tableaux Systems
  • Internal note : Maybe this file need a better style. Specially the proofs.
 
  • inria-00281631, version 1
  • oai:hal.inria.fr:inria-00281631
  • From: 
  • Submitted on: Saturday, 24 May 2008 11:06:58
  • Updated on: Saturday, 24 May 2008 11:47:14
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