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Reductions in Intuitionistic Linear Logic

Published online by Cambridge University Press:  04 March 2009

Sergei Soloviev
Sergei Soloviev
Affiliation:
St.Petersburg Institute for Informatics of the Russian Academy of Sciences (SPIIRAN), 199178, St.Petersburg, 14-th line, 39, Email sergei@iias.spb.su or soloviev@daimi.aau.dk
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Abstract

In this work we show how some useful reductions known from ordinary intuitionistic propositional calculus can be modified for Intuitionistic Linear Logic (without modalities). The main reductions we consider are: (1) the reduction of the depth of formulas in the sequents by addition of new variables, and (2) the elimination of linear disjunction, tensor and constant F. Both transformations preserve deducibility, that is, a transformed sequent is deducible if and only if the initial one was deducible. The size of the sequent grows linearly in case (1) and ≤ On8 in case (2).

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 5 , Issue 4 , December 1995 , pp. 483 - 499
Copyright
Copyright © Cambridge University Press 1995

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