WPE & TME: Semantic Calculus Languages
WPE (Wave Pattern Encoding) and TME (Temporal Modulation Encoding) are innovative text-native languages designed for explicit semantic structure and temporal reasoning. These languages serve as mathematical notations for complex systems, moving beyond traditional equations to facilitate a deeper understanding of relationships and interactions within systems.

The Challenge

Current large language models (LLMs) primarily rely on statistical reasoning. Although they encode vast amounts of implicit structure within billions of parameters, critical challenges remain:

• Internal representation inspection is impossible.
• Debugging reasoning chains is unfeasible.
• Explicit relationship modification is not allowed.
• Temporal connections are relied upon inference rather than direct encoding.

The WPE/TME Solution

WPE and TME address these issues by making structural relationships clear through a robust 4-parameter geometric encoding:

Component:Domain:Shell@Phase|Curvature

This transparency ensures that each relationship is explicitly visible, eliminating hidden complexities.

Usage Examples

Feedback Control Loop

Here's how components are defined in WPE:

Sensor:P:2@0|-3.0        # Physics domain, shell 2
Controller:C:3@90|-2.5    # Cognition domain, shell 3
Actuator:P:4@180|-2.0     # Physics domain, shell 4

Sensor <-> Controller     # cos(90° - 0°) = 0.0 (orthogonal relationship)
Controller <-> Actuator   # cos(180° - 90°) = 0.0 (orthogonal)
Actuator <-> Sensor       # cos(0° - 180°) = -1.0 (opposition, indicating feedback)

Multi-Agent System

WPE makes relationships among agents explicit:

Agent1:C:2@0|-2.5
Agent2:C:2@120|-2.5
Agent3:C:2@240|-2.5

The geometry of phase positions generates automatic coupling, ensuring balanced interactions among agents.

Temporal Sequence with TME

The TME syntax directly represents temporal sequences:

@temporal_scale α=1.0
T1: Initialize:P:1@0|-3.0 [duration=5]
T2: Process:C:2@45|-2.5 [duration=10] 
T3: Output:O:3@90|-2.0 [duration=3]
T1 -> T2 -> T3  # Sequential flow in time

Language Specification

The geometric encoding utilizes four key parameters:

Coupling strengths are determined based on angular differences:

Coupling_strength = cos(θᵢ - θⱼ)

Applications

LLM Scaffolding

WPE can explicitly encode reasoning steps for improved structure in LLMs, allowing better tracking of arguments.

System Modeling

WPE and TME enable the detailed modeling of complex systems, incorporating feedback, hierarchy, and temporal dynamics for comprehensive analysis.

Conclusion

WPE and TME provide a powerful framework for semantic encoding, making relationships explicit and more manageable. These languages are poised to advance various applications in AI, including LLM scaffolding, multi-agent systems, and temporal reasoning. For extensive documentation and additional resources, the language specifications, example codes, and implementation details can be found in the project's README.