# Display to Labeled Proofs and Back Again for Tense Logics

arXiv: https://arxiv.org/abs/1911.02289 · HTML: https://mlsanity.com/paper/1911.02289/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2019.

## Built on by (most cited first, 1 of 1)

- [Constructive Interpolation and Concept-Based Beth Definability for Description Logics via Sequents](https://mlsanity.com/paper/2404.15840/) (2024)

## Abstract (arXiv)

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is translatable to a derivation in the associated display calculus. A key insight in this converse translation is a canonical representation of display sequents as labeled polytrees. Labeled polytrees, which represent equivalence classes of display sequents modulo display postulates, also shed light on related correspondence results for tense logics.