# Rooted Hypersequent Calculus for Modal Logic S5

## TL;DR

This paper introduces a rooted hypersequent calculus for modal logic S5, demonstrating its invertibility, admissibility of key rules, and establishing soundness and completeness.

## Contribution

It presents a novel calculus for S5 with invertible rules and proves its soundness and completeness, advancing proof theory for modal logic.

## Key findings

- All rules are invertible.
- Weakening, contraction, and cut are admissible.
- Soundness and completeness are established.

## Abstract

We present a rooted hypersequent calculus for modal propositional logic S5. We show that all rules of this calculus are invertible and that the rules of weakening, contraction, and cut are admissible. Soundness and completeness are established as well.