In practice, we implement interaction probability within the CAS-6 tensor (Section 3.3) as:
Iij(3)=Pij=fij+rij+eijI_{ij}^{(3)} = P = f + r + e
This allows the probability axis to remain differentiable and learnable within an LLM's architecture while preserving multi-factorial semantics.
By decoupling interaction probability from mere frequency and enriching it with semantic resonance and predictive entanglement, the CAS-6 model captures deeper, cognitively aligned patterns in language. This redefinition is pivotal in advancing LLMs toward true interpretive AI, capable of understanding subtle meaning beyond word counts.
3.5 Interaction Weight: Inhibition, Synergy, and Semiotic Tension
While interaction probability (Section 3.4) captures how likely a word pair or triad is to co-occur meaningfully, interaction weight introduces a critical qualitative axis: the valence or directional effect of that interaction on the final semantic construction. Within the CAS-6 framework, we model this as a continuous variable ranging from 2 (strongly inhibitive) to +2 (strongly synergistic), enabling AI models to infer how word interactions construct or destruct potential meaning spaces.
A. Conceptual Foundation: From Syntax to Semiosis
In classical linguistics and cognitive semantics, meaning emerges not merely from presence but from relational force between concepts (Lakoff & Johnson, 1980). For instance:
The phrase "stone heart" combines two denotatively unrelated concepts.
Yet their interplay leads to a powerful metaphor of emotional coldness.
In this case, "stone" inhibits the affective openness of "heart"---yielding a highly loaded figurative meaning.
This semiotic tension, marked by a negative interaction weight, is a source of both complexity and aesthetic depth. On the other hand:
"gentle breeze" represents a synergistic pairing, where both components reinforce a shared semantic domain (calmness, nature, softness).
B. Formal Definition of Interaction Weight (w)
Let each directed interaction between word i and word j carry a weight:
