Recognizing and leveraging these levels allows AI models to traverse beyond syntax and probability, entering realms where emotion, irony, symbolism, and beauty reside---a capability critical for advanced human-AI linguistic interaction.
3.3 Visual Representation and Lightweight Mathematics
To operationalize the CAS-6 framework in machine learning systems, we propose lightweight yet expressive formalizations of word interaction patterns using graph theory and tensor representations. These mathematical abstractions serve as scaffolds for visualizing, modeling, and computing interaction-driven semantics, particularly beyond the capabilities of standard token-sequence models.
A. Interaction Patterns as Graph Structures
We model each interaction as a directed labeled graph, in which:
Nodes (V) represent individual lexical units (e.g., tears, eyes, crocodile).
Edges (E) represent semantic or syntactic interactions between these units.
Edge attributes encode:
Directionality (who influences whom),
Weight (synergistic vs. inhibitive interaction),
Stability (temporal or contextual resonance),
Interaction probability (contextual co-occurrence score).
Example: Triadic Interaction Graph
Given the phrase "crocodile tears eyes", we can construct:
V = {v: tears, v: eyes, v: crocodile}
E = { (v v), (v v), (v v) }
Each edge can have associated metadata:
Weight [2, +2]
Stability [0, 1]
Probability [0, 1]
Figure 1 (hypothetical):
   [crocodile]
      Â
