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 | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,679 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesSimona Ronchi della Rocca & Luca Roversi (1997). Lambda Calculus and Intuitionistic Linear Logic. Studia Logica 59 (3):417-448.
Andreja Prijatelj (1995). Connectification Forn-Contraction. Studia Logica 54 (2):149 - 171.
Peter W. O'Hearn & David J. Pym (1999). The Logic of Bunched Implications. Bulletin of Symbolic Logic 5 (2):215-244.
Simone Martini & Andrea Masini (1994). A Modal View of Linear Logic. Journal of Symbolic Logic 59 (3):888-899.
Andreja Prijatelj (1995). Reflections on “Difficult” Embeddings. Journal of Philosophical Logic 24 (1):71 - 84.
Simona Ronchi Della Rocca & Luca Roversi (1997). Lambda Calculus and Intuitionistic Linear Logic. Studia Logica 59 (3):417-448.
Daniele Porello (2012). Incompatibility Semantics From Agreement. Philosophia 40 (1):99-119.
Mitsuhiro Okada & Kazushige Terui (1999). The Finite Model Property for Various Fragments of Intuitionistic Linear Logic. Journal of Symbolic Logic 64 (2):790-802.
Fernando Ferreira (2008). A Most Artistic Package of a Jumble of Ideas. Dialectica 62 (2: Table of Contents"/> Select):205–222.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads9 ( #114,063 of 549,088 )Recent downloads (6 months)1 ( #63,317 of 549,088 )How can I increase my downloads? |
My notes
Discussion
