Dimensional Logic for LLM Output Selection

This repository contains a proof-of-concept implementation of applying Dimensional Logic (σ₂, μ₃, κ₄) to large language model (LLM) outputs.
The goal is to improve reflexivity (reasoning about reasoning) and context coherence when selecting between candidate answers generated by an LLM.

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🔍 Background

Classical logic evaluates statements in binary terms (true/false).
Dimensional Logic extends this by introducing additional operators:

• σ₂ (Systematic Derivation) – ensures structural consistency in reasoning
• μ₃ (Reflexivity) – models recursive awareness of reasoning steps
• κ₄ (Context Coherence) – evaluates how well reasoning fits into a broader context

This framework allows us to score and re-rank LLM responses not only by surface plausibility but also by epistemic depth.

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📂 Repository Contents

• dimensional_llm_selector_en.py → Python implementation of dimensional scoring and selection
• (optional) Example CSV / heatmap → demo results from a toy experiment

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🚀 Usage

1. Clone this repo:

   git clone https://github.com/yourusername/dimensional-logic-llm-selector.git
   cd dimensional-logic-llm-selector

2. Run the script with sample outputs:

   from dimensional_llm_selector_en import dimensional_score, select_best_response
   
   outputs = [
       "The capital of France is Paris.",
       "The capital of France is Lyon.",
       "The capital of France is Madrid."
   ]
   
   context = "Geography, European capitals"
   
   best = select_best_response(outputs, context)
   print("Best response:", best)

3. Example output:

   Best response: The capital of France is Paris.
   

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📊 How It Works

Each LLM response is scored as:

Score = α · μ₃(response, others) + β · κ₄(response, context)

• μ₃: Reflexive alignment – does the answer make sense relative to others?
• κ₄: Contextual coherence – does the answer fit into the given context?
• α, β: Tunable weights to balance reflexivity and coherence.

If the dimensional score passes a threshold, the response is preferred over naive likelihood-based ranking.

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🧠 Applications

• More reliable multi-agent reasoning
• Reducing hallucinations in LLMs by epistemic filtering
• Extending game theory and decision theory with reflexive/contextual dimensions
• Foundations for epistemic-aware AI systems

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📜 License

MIT License – free to use, modify, and share.

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📖 References

• Stegemann, W. (2025). *Dimensional Mathematics: An Axiomatic Extension of Epistemic Relativity. https://doi.org/10.5281/zenodo.16911643