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.
Recommended Citation
Galatos, N. & Jipsen, P. Distributive residuated frames and generalized bunched implication algebras. Algebra Univers. (2017) 78: 303. https://doi.org/10.1007/s00012-017-0456-x
Peer Reviewed
1
Copyright
Springer
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.