This white paper introduces the concept of a Semantic Geometry Dictionary (SGD), a structured system that encodes abstract concepts into mathematical formulas using variable-driven frameworks. The goal is to enable interpretability, causal reasoning, and simulation of meaning within AI systems, decision-making tools, educational environments, and conceptual modeling.
In contrast to black-box neural networks, the SGD offers a transparent, symbolic approach that reflects how abstract terms like “wisdom,” “flow,” or “unification” are constructed, influenced, and modified by their components. Each concept is defined by 2, 3, or more variables, each marked with a “(+)” or “(-)” to indicate positive or negative influence, and is accompanied by a canonical equation that represents the concept in its operational form.
The dictionary allows for a variable number of dimensions per concept. Some require just two dimensions for operational clarity (e.g., trust = consistency / volatility), while others demand richer, multidimensional representations. This flexibility supports different levels of modeling depth and semantic granularity.
By linking concepts to functional equations, the SGD enables practical use in interpretable AI and conceptual modeling—bridging theoretical insight and application [1], [3]—in applications such as interpretable AI, ethical simulations, educational modeling, philosophical reasoning, and value-driven system design. It allows human language to be formalized without reducing its expressive richness.
This system also supports real-time diagnostics, intervention design, and explanation generation. Instead of vague references to “alignment” or “purpose,” systems powered by the SGD can refer to the precise mathematical structures driving those qualities.
Ultimately, the Semantic-Mathematical Dictionary aims to provide an extensible conceptual infrastructure for computational reasoning, narrative design, institutional modeling, and educational synthesis. It is not a replacement for natural language but a bridge between human understanding and formal expression.