# Intuitionistic Non-Normal Modal Logics: A general framework

arXiv: https://arxiv.org/abs/1901.09812 · HTML: https://mlsanity.com/paper/1901.09812/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2019.

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

- [From Knowledge to Conjectures: A Modal Framework for Reasoning about Hypotheses](https://mlsanity.com/paper/2508.07304/) (2025)

## Abstract (arXiv)

We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider the more important case of bimodal logics, which contain both modal operators. In this case we define several interactions between Necessity and Possibility of increasing strength, although weaker than duality. For all logics we provide both a Hilbert axiomatisation and a cut-free sequent calculus, on its basis we also prove their decidability. We then give a semantic characterisation of our logics in terms of neighbourhood models. Our semantic framework captures modularly not only our systems but also already known intuitionistic non-normal modal logics such as Constructive K (CK) and the propositional fragment of Wijesekera's Constructive Concurrent Dynamic Logic.