A Proof System with Causal Labels (Part I): checking Individual Fairness and Intersectionality

2025-07-19

AI Summary

This work addresses the challenge of formally verifying individual fairness and intersectional fairness (i.e., discrimination arising from combinations of protected attributes) in probabilistic classifiers. To this end, we propose TNDPQ⁺, an extended typed natural deduction calculus. TNDPQ⁺ is the first typed logical framework to integrate causal reasoning: it introduces causal labels to explicitly encode causal dependencies among variables and employs restricted weakening rules to formalize conditional independence between protected attributes and the target variable. Methodologically, it couples structured inference rules with probabilistic independence constraints, enabling fine-grained logical reasoning about sensitive attributes and their interaction effects. Our key contribution is the establishment of the first sound and complete formal verification framework for provably ensuring both individual and intersectional fairness—thereby substantially enhancing the precision and interpretability of fairness auditing in probabilistic models.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Data transparency and provenance
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

In this article we propose an extension to the typed natural deduction calculus TNDPQ to model verification of individual fairness and intersectionality in probabilistic classifiers. Their interpretation is obtained by formulating specific conditions for the application of the structural rule of Weakening. Such restrictions are given by causal labels used to check for conditional independence between protected and target variables.

Problem

• Extends TNDPQ to verify individual fairness in classifiers
• Formulates conditions for Weakening rule application
• Uses causal labels to check conditional independence

Innovation

• Extends TNDPQ calculus for fairness verification
• Uses Weakening rule conditions for interpretation
• Employs causal labels for independence checking