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.


    Volume: Volume 7, Issue 1
    Published on: March 27, 2011
    Imported on: March 10, 2010
    Keywords: Computer Science - Logic in Computer Science,03F10, 03F52, 03F55
    Funding:
      Source : OpenAIRE Graph
    • Functional interpretations of arithmetic and analysis; Code: PTDC/MAT/104716/2008
    • INTERPRETAÇÕES FUNCIONAIS E SUAS APLICAÇÕES; Code: SFRH/BPD/34527/2006

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