# Modelling socio-political competition

## TL;DR

This paper develops a new many-valued modal logic framework with enriched relational semantics to model complex socio-political competition, including political promises and social demands.

## Contribution

It introduces a novel many-valued, multi-type modal language with enriched relational semantics and provides axiomatization and completeness results for modeling socio-political interactions.

## Key findings

- Successfully axiomatized the logic of socio-political competition.
- Proved completeness theorem for the proposed logic.
- Demonstrated application through a case study of political and social interactions.

## Abstract

This paper continues the investigation of the logic of competing theories, be they scientific, social, political etc. We introduce a many-valued, multi-type modal language which we endow with relational semantics based on enriched reflexive graphs, inspired by Plo\v{s}\v{c}ica's representation of general lattices. We axiomatize the resulting many-valued, non-distributive modal logic of these structures and prove a completeness theorem. We illustrate the application of this logic through a case study in which we model competition among interacting political promises and social demands within an arena of political parties social groups.