Skip to Main content Skip to Navigation
Journal articles

A framework for proof systems

Nigam Vivek 1 Dale Miller 1, 2
2 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : Linear logic can be used as a meta-logic to specify a range of object-level proof systems. In particular, we show that by providing different polarizations within a focused proof system for linear logic, one can account for natural deduction (normal and non-normal), sequent proofs (with and without cut), and tableaux proofs. Armed with just a few, simple variations to the linear logic encodings, more proof systems can be accommodated, including proof system using generalized elimination and generalized introduction rules. In general, most of these proof systems are developed for both classical and intuitionistic logics. By using simple results about linear logic, we can also give simple and modular proofs of the soundness and relative completeness of all the proof systems we consider.
Document type :
Journal articles
Complete list of metadata

https://hal.inria.fr/hal-00772562
Contributor : Dale Miller <>
Submitted on : Thursday, January 10, 2013 - 5:15:29 PM
Last modification on : Thursday, January 7, 2021 - 3:40:14 PM
Long-term archiving on: : Thursday, April 11, 2013 - 4:07:52 AM

File

nigam-ijcar.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00772562, version 1

Collections

Citation

Nigam Vivek, Dale Miller. A framework for proof systems. Journal of Automated Reasoning, Springer Verlag, 2010, 45 (2). ⟨hal-00772562⟩

Share

Metrics

Record views

294

Files downloads

153