# On How Kelsenian Jurisprudence and Intuitionistic Logic help to avoid Contrary-to-Duty paradoxes in Legal Ontologies

## TL;DR

This paper demonstrates how integrating Kelsenian jurisprudence with intuitionistic logic, specifically an intuitionistic description logic, can effectively prevent contrary-to-duty paradoxes in legal ontologies by modeling valid legal statements.

## Contribution

It introduces an intuitionistic version of ALC logic, iALC, to model legal statements and avoid CTD paradoxes, bridging legal philosophy and formal logic.

## Key findings

- iALC successfully models legal statements avoiding CTDs
- The approach provides consistent legal ontologies free of paradoxes
- Legal models based on iALC can handle complex legal reasoning

## Abstract

In this article we show how Hans Kelsen jurisprudence and Intuitionistic logic are used to avoid the well-known contrary-to-duty (CTD) paradoxes, such as Chisholm paradoxes and its variants. This article uses an intuitionistic version of the ALC description logic, named iALC, to show how an ontology based on individually valid legal statements is able to avoid CTDs by providing models to them.