Iterative division in the Distributive Full Non-associative Lambek Calculus
Igor Sedl\'ar
TL;DR
This paper introduces an extension of the Distributive Full Non-associative Lambek Calculus with iterative division operators, providing a complete axiomatization and proving decidability through finite model property.
Contribution
It presents the first complete axiomatization and decidability proof for the extended calculus with iterative division operators.
Findings
Complete axiomatization of the extended calculus
Decidability established via finite model property
Representation of iterative composition in linguistic resources
Abstract
We study an extension of the Distributive Full Non-associative Lambek Calculus with iterative division operators. The iterative operators can be seen as representing iterative composition of linguistic resources or of actions. A complete axiomatization of the logic is provided and decidability is established via a proof of the finite model property.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.