Gilda Ferreira ; Paulo Oliva - Functional Interpretations of Intuitionistic Linear Logic

lmcs:1110 - Logical Methods in Computer Science, March 27, 2011, Volume 7, Issue 1 - https://doi.org/10.2168/LMCS-7(1:9)2011
Functional Interpretations of Intuitionistic Linear LogicArticle

Authors: Gilda Ferreira ORCID; Paulo Oliva

We present three different functional interpretations of intuitionistic linear logic ILL and show how these correspond to well-known functional interpretations of intuitionistic logic IL via embeddings of IL into ILL. The main difference from previous work of the second author is that in intuitionistic linear logic (as opposed to classical linear logic) the interpretations of !A are simpler and simultaneous quantifiers are no longer needed for the characterisation of the interpretations. We then compare our approach in developing these three proof interpretations with the one of de Paiva around the Dialectica category model of linear logic.

https://doi.org/10.2168/LMCS-7(1:9)2011
Source: arXiv.org:1012.1174
Volume: Volume 7, Issue 1
Secondary volumes: Selected Papers of the 23rd International Workshop on Computer Science Logic and the 18th Annual Conference of the EACSL (CSL 2009)
Published on: March 27, 2011
Imported on: March 10, 2010
Keywords: Computer Science - Logic in Computer Science, 03F10, 03F52, 03F55
Licence: arXiv.org - Non-exclusive license to distribute
Funding:
    Source : OpenAIRE Graph
  • Functional interpretations of arithmetic and analysis; Funder: Fundação para a Ciência e a Tecnologia, I.P.; Code: PTDC/MAT/104716/2008
  • INTERPRETAÇÕES FUNCIONAIS E SUAS APLICAÇÕES; Funder: Fundação para a Ciência e a Tecnologia, I.P.; Code: SFRH/BPD/34527/2006

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