Functional interpretations of intuitionistic linear logic

Authors:
Gilda Ferreira;Paulo Oliva
Affiliations:
School of Electronic Engineering and Computer Science, Queen Mary, University of London;School of Electronic Engineering and Computer Science, Queen Mary, University of London
Venue:
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Year:
2009

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Abstract

We present three functional interpretations of intuitionistic linear logic and show how these correspond to well-known functional interpretations of intuitionistic logic via embeddings of ILω into ILLω. The main difference from previous work of the second author is that in intuitionistic linear logic the interpretations of !A are simpler (at the cost of an asymmetric interpretation of pure ILLω) and simultaneous quantifiers are no longer needed for the characterisation of the interpretations.