Decomposition of Reduction

  • Ernst ZimmermannEmail author
Part of the Trends in Logic book series (TREN, volume 39)


The method of decomposition of reduction is presented for proofs of confluence and termination in rewriting and natural deduction. It is shown that any subclass of reductions, which is locally confluent and terminating and commutes with the full reduction in a specific way, transfers confluence and termination to the full reduction. The method is introduced on a pure rewriting level and subsequently applied to natural deduction, i.e. its calculi for Intuitionistic Logic and Intuitionistic Linear Logic, where respective subclasses of reductions are shown to exist. A key observation is that local confluence holds for reductions in natural deduction.


Intuitionistic Linear Logic Natural Deduction Local Meetings Transfers Confluence Subdeduction 
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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.DFG and ANR Project Hypotheses, Wilhelm-Schickard-InstitutUniversität TübingenTübingenGermany

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