Ferreira, Gilda and Oliva, Paulo - Functional Interpretations of Intuitionistic Linear Logic

lmcs:1110 - Logical Methods in Computer Science, March 27, 2011, Volume 7, Issue 1
Functional Interpretations of Intuitionistic Linear Logic

Authors: Ferreira, Gilda and Oliva, Paulo

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.

Source : oai:arXiv.org:1012.1174
DOI : 10.2168/LMCS-7(1:9)2011
Volume: Volume 7, Issue 1
Published on: March 27, 2011
Submitted on: March 10, 2010
Keywords: Computer Science - Logic in Computer Science,03F10, 03F52, 03F55


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