Functional Interpretations of Intuitionistic Linear Logic

Details Functional Interpretations of Intuitionistic Linear Logic Functional Interpretations of Intuitionistic Linear Logic

2010-12-06

arxiv.org/abs/1012.1174v2

LMCS 7 (1:9) 2011

Computer Science

Logic in Computer Science

Scientific paper

10.2168/LMCS-7(1:9)2011

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.

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