# Non normal logics: semantic analysis and proof theory

## TL;DR

This paper develops proper display calculi for various non-normal modal logics, ensuring soundness, completeness, and desirable proof-theoretic properties through a semantic and multi-type approach.

## Contribution

It introduces a novel semantic analysis and multi-type methodology to design display calculi for non-normal modal logics, extending proof-theoretic tools.

## Key findings

- Calculi are sound and complete
- Calculi enjoy cut elimination and subformula property
- Framework applies to multiple non-normal modal logics

## Abstract

We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our proposal applies the multi-type methodology in the design of display calculi, starting from a semantic analysis based on the translation from monotonic modal logic to normal bi-modal logic.