# On the Correspondence between Nested Calculi and Semantic Systems for Intuitionistic Logics

arXiv: https://arxiv.org/abs/2104.09215 · HTML: https://mlsanity.com/paper/2104.09215/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2021.

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

- [Automating Reasoning with Standpoint Logic via Nested Sequents](https://mlsanity.com/paper/2205.02749/) (2022)

## Abstract (arXiv)

This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting's nested calculi naturally arise from their corresponding labelled calculi--for each of the aforementioned logics--via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic's semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic's semantics.