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The undecidability of second order linear logic without exponentials

Published online by Cambridge University Press:  12 March 2014

Yves Lafont
Yves Lafont*
Affiliation:
Laboratoire de Mathématiques Discrètes, UPR 9016 du CNRS, 163 Avenue de Luminy, Case 930, 13288 Marseille Cedex 9, France, E-mail: lafont@lmd.univ-mrs.fr
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Abstract

Recently, Lincoln, Scedrov and Shankar showed that the multiplicative fragment of second order intuitionistic linear logic is undecidable, using an encoding of second order intuitionistic logic. Their argument applies to the multiplicative-additive fragment, but it does not work in the classical case, because second order classical logic is decidable. Here we show that the multiplicative-additive fragment of second order classical linear logic is also undecidable, using an encoding of two-counter machines originally due to Kanovich. The faithfulness of this encoding is proved by means of the phase semantics.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 2 , June 1996 , pp. 541 - 548
Copyright
Copyright © Association for Symbolic Logic 1996

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References

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