Document Type
Article
Publication Date
1-17-2024
Abstract
In this article, we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics). Specifically, we generalize the residuated frames in Reference [34] to arbitrary signatures of normal lattice expansions (LE). Such a generalization provides a valuable tool for proving important properties of LE-logics in full uniformity. We prove semantic cut elimination for the display calculi D.LE associated with the basic normal LE-logics and their axiomatic extensions with analytic inductive axioms. We also prove the finite model property (FMP) for each such calculus D.LE, as well as for its extensions with analytic structural rules satisfying certain additional properties.
Recommended Citation
Giuseppe Greco, Peter Jipsen, Fei Liang, Alessandra Palmigiano, and Apostolos Tzimoulis. 2024. Algebraic Proof Theory for LE-logics. ACM Trans. Comput. Logic 25, 1, Article 6 (January 2024), 37 pages. https://doi.org/10.1145/3632526
Peer Reviewed
1
Copyright
The authors
Comments
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in ACM Transactions on Computational Logic, volume 25, issue 1, in 2024 following peer review. This article may not exactly replicate the final published version. The definitive publisher-authenticated version is available online at
https://doi.org/10.1145/3632526