Modeling Legal Integrity Using Plithogenic
n-SuperHyperGraphs: A Multidimensional Representation of Moral Coherence in Dworkin's Theory

 

Carmen Marina Méndez Cabrita^1,*, Josía Jeseff Isea Argüelles² , Luis Andrés Crespo Berti³ , María Elena Infante Miranda⁴

¹Universidad Regional Autónoma de los Andes (UNIANDES), Ecuador

Emails: ut.carmenmmc56@uniandes.edu.ec; ui.josiaia82@uniandes.edu.ec; ui.luiscrespo@uniandes.edu.ec; ui.mariainfante@uniandes.edu.ec

 

 

Abstract

This project aims to concretize Ronald Dworkin's theory of legal integrity via Plithogenic n-SuperHyperGraphs. Therefore it investigates how such mathematical entities metaphorically and multidimensionally formulate moral coherence in legal interpretation. Using a mixed-method approach, this work will assess documents through a documentary assessment of Dworkin's written works (Law’s Empire and Taking Rights Seriously) to formulate a Plithogenic n-SuperHyperGraph of a case study featuring n-dimensional nodes as moral principles, moral assertions, and past decisions with hyperedges symbolizing the relationship between them generated by degrees of truth, falsity, or indeterminacy. Tools of graph visualization and neutrosophic computing will provide the legal assessment of characterization for coherence. The results will discuss whether the model intentionally visualizes the connections among the principles and how it assessed which characterizations would make the law most morally coherent under Dworkin's theory while acknowledging the indeterminacy in certain complicated cases. Thus, this study seeks to find correlations between which nodes function as the primary principles consistent with Dworkin's metaphor of the law's "chain." Ultimately, this research intends to present Plithogenic n-SuperHyperGraphs as a viable application to formally express Dworkin's theory for the sake of more moral legal determinations applicable to legal education or judicial assistive software, although generalizability will require cross-jurisdictional applications of the model.

Keywords: Dworkin; Legal Integrity; N- Superhypergraphs; Moral Coherence; Judicial Interpretation; Neutrosophic; Plithogenic