The Relational Calculus for Green AI

Relational Calculus is a research project introducing a domain-agnostic framework for representing complex systems through dimensionless, intrinsic relationships rather than absolute quantities. The core premise is that many physical, computational, and informational systems are better characterized by their internal proportions relative to a global capacity than by their raw magnitudes. This transformation separates structure from scale, enabling models and analyses to operate on invariant geometric properties rather than environment-dependent values. The project explores both the theoretical foundations and practical implications of this representation across multiple domains, including: - High Energy Physics (scale-invariant kinematics and jet tagging) - Machine Learning (robustness to distribution shift and zero-shot transfer) - Complex systems and dynamical processes Preliminary results indicate that relational representations can: - improve generalization across varying scales - reduce sensitivity to covariate shift - significantly lower computational requirements by simplifying problem structure Rather than proposing a new model architecture, Relational Calculus is positioned as a pre-representational layer that can be integrated with existing methods, including statistical models, deep learning systems, and agent-based frameworks. This OSF project serves as a central hub for: - theoretical development of the framework - domain-specific applications - datasets and experimental results - code implementations and reproducibility resources The long-term objective is to establish Relational Calculus as a unifying principle for scale-invariant modeling, enabling more efficient, generalizable, and interpretable approaches to scientific and artificial intelligence systems.