An analysis of gödel's dialectica interpretation via linear logic

Dialectica 62 (2):269–290 (2008)
Abstract
This article presents an analysis of Gödel's dialectica interpretation via a refinement of intuitionistic logic known as linear logic. Linear logic comes naturally into the picture once one observes that the structural rule of contraction is the main cause of the lack of symmetry in Gödel's interpretation. We use the fact that the dialectica interpretation of intuitionistic logic can be viewed as a composition of Girard's embedding of intuitionistic logic into linear logic followed by de Paiva's dialectica interpretation of linear logic. We then investigate the various properties of the dialectica interpretation, such as the characterisation theorem, and variants of Gödel's interpretation within the linear logic context. The role of contraction in extensions to classical logic, arithmetic and analysis is also discussed.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 11,808
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA
Mircea-Dan Hernest & Trifon Trifonov (2010). Light Dialectica Revisited. Annals of Pure and Applied Logic 161 (11):1379-1389.
Gilda Ferreira & Paulo Oliva (2012). On Bounded Functional Interpretations. Annals of Pure and Applied Logic 163 (8):1030-1049.
Similar books and articles
Analytics

Monthly downloads

Added to index

2009-01-28

Total downloads

22 ( #81,677 of 1,099,788 )

Recent downloads (6 months)

11 ( #21,120 of 1,099,788 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.