Document Type

Article

Publication Date

10-9-2017

Abstract

We show that all extensions of the (non-associative) Gentzen system for distributive full Lambek calculus by simple structural rules have the cut elimination property. Also, extensions by such rules that do not increase complexity have the finite model property, hence many subvarieties of the variety of distributive residuated lattices have decidable equational theories. For some other extensions, we prove the finite embeddability property, which implies the decidability of the universal theory, and we show that our results also apply to generalized bunched implication algebras. Our analysis is conducted in the general setting of residuated frames.

Comments

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Algebra Universalis, volume 78, in 2017 following peer review. The final publication is available at Springer via DOI: 10.1007/s00012-017-0456-x.

Peer Reviewed

1

Copyright

Springer

Available for download on Tuesday, October 09, 2018

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Algebra Commons

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