The formal logic of interaction

This paper introduces the formal logic of interaction, a framework inspired by set-theoretic ideas such as inclusion–exclusion, commutativity, associativity, and distributivity. It establishes a formal model for composition and interaction, enabling precise analysis of relationships in complex systems. Core properties—including operational rules and quantitative measures—are systematically developed, providing mathematical tools for characterizing interactions. As a brief illustration, the framework is applied to chemical systems, where total energy and potential energy in multi-atomic or molecular systems can be decomposed into single-body contributions and interaction terms of increasing order, expressed in a simple form and with the potential to simplify calculations.