algebra universalis

, Volume 54, Issue 4, pp 449–463

A Gentzen system for involutive residuated lattices

Original Paper

DOI: 10.1007/s00012-005-1957-6

Cite this article as:
Wille, A.M. Algebra univers. (2005) 54: 449. doi:10.1007/s00012-005-1957-6


We establish a cut-free Gentzen system for involutive residuated lattices and provide an algebraic proof of completeness. As a result we conclude that the equational theory of involutive residuated lattices is decidable. The connection to noncommutative linear logic is outlined.

2000 Mathematics Subject Classification.

06F05 06D35 06F15 03G10 

Keywords and phrases.

Gentzen System residuated lattice involutive residuated lattice linear logic equational theory 

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany

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