# Modularisation of Sequent Calculi for Normal and Non-normal Modalities

## TL;DR

This paper develops modular linear nested sequent calculi for a broad class of normal and non-normal modal logics, including dependent multimodal logics, enhancing proof search and derivation analysis.

## Contribution

It introduces local versions of sequent rules to create modular nested calculi for various modal logics, including the first for dependent multimodal logics.

## Key findings

- First nested sequent calculi for dependent multimodal logics
- Modular systems with separate modal rules
- Linear nested calculi can be restricted to ordinary sequent derivations

## Abstract

In this work we explore the connections between (linear) nested sequent calculi and ordinary sequent calculi for normal and non-normal modal logics. By proposing local versions to ordinary sequent rules we obtain linear nested sequent calculi for a number of logics, including to our knowledge the first nested sequent calculi for a large class of simply dependent multimodal logics, and for many standard non-normal modal logics. The resulting systems are modular and have separate left and right introduction rules for the modalities, which makes them amenable to specification as bipole clauses. While this granulation of the sequent rules introduces more choices for proof search, we show how linear nested sequent calculi can be restricted to blocked derivations, which directly correspond to ordinary sequent derivations.