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Text-to-State Mapping for Non-Resolution Reasoning: The Contradiction-Preservation Principle

Kei Saito

TL;DR

...

Abstract

Non-Resolution Reasoning (NRR) provides a formal framework for maintaining semantic ambiguity rather than forcing premature interpretation collapse. While the foundational architecture establishes state spaces and operators for ambiguity-preserving computation, the critical question of how natural language maps to these mathematical structures remains open. This paper introduces the text-to-state mapping function φ that transforms linguistic input into superposition states within the NRR framework. We formalize the Contradiction-Preservation Principle, which requires that genuinely ambiguous expressions maintain non-zero entropy in their state representations, and develop extraction protocols using existing Large Language Models as interpretation generators. Empirical validation across 68 test sentences spanning lexical, structural, and pragmatic ambiguity demonstrates that our mapping achieves mean Shannon entropy H(S) = 1.087 bits for ambiguous inputs while baseline single-interpretation approaches yield H(S) = 0.000. The framework provides the missing algorithmic bridge between raw text and the formal state spaces on which NRR operators act, enabling architectural collapse deferment in language model inference.

Text-to-State Mapping for Non-Resolution Reasoning: The Contradiction-Preservation Principle

TL;DR

...

Abstract

Non-Resolution Reasoning (NRR) provides a formal framework for maintaining semantic ambiguity rather than forcing premature interpretation collapse. While the foundational architecture establishes state spaces and operators for ambiguity-preserving computation, the critical question of how natural language maps to these mathematical structures remains open. This paper introduces the text-to-state mapping function φ that transforms linguistic input into superposition states within the NRR framework. We formalize the Contradiction-Preservation Principle, which requires that genuinely ambiguous expressions maintain non-zero entropy in their state representations, and develop extraction protocols using existing Large Language Models as interpretation generators. Empirical validation across 68 test sentences spanning lexical, structural, and pragmatic ambiguity demonstrates that our mapping achieves mean Shannon entropy H(S) = 1.087 bits for ambiguous inputs while baseline single-interpretation approaches yield H(S) = 0.000. The framework provides the missing algorithmic bridge between raw text and the formal state spaces on which NRR operators act, enabling architectural collapse deferment in language model inference.
Paper Structure (55 sections, 1 theorem, 13 equations, 3 figures, 5 tables, 2 algorithms)

This paper contains 55 sections, 1 theorem, 13 equations, 3 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. The Early Semantic Commit Problem
  3. Softmax Normalization.
  4. Autoregressive Generation.
  5. Training Objectives.
  6. Non-Resolution Reasoning
  7. Contributions
  8. Paper Organization
  9. Related Work
  10. Uncertainty in LLM Inference
  11. Multi-Hypothesis Approaches
  12. Ambiguity in NLP
  13. Relation to NRR Framework
  14. Formal Framework
  15. Preliminary Definitions
  16. ...and 40 more sections

Key Result

Theorem 1

For any text $T$ with $|\mathcal{I}(T)| > 1$ distinct extractable interpretations, the mapping $\phi$ produces a state $S$ such that:

Figures (3)

  • Figure 1: Test set composition across five ambiguity categories (68 sentences total). Rule-based extraction targets adversative and hedging categories with both English and Japanese sentences. LLM-based extraction targets epistemic, lexical, and structural categories with English sentences only.
  • Figure 2: LLM-based extraction results across three models (GPT-4, Gemini, Claude) for English sentences. The dashed line indicates $H_{\max} = 1.0$ for binary interpretations. All models achieve $H > 0$ across all categories, with epistemic showing the highest entropy due to multiple interpretive layers.
  • Figure 3: Combined experimental results. (A) State entropy $H(S)$ by category, showing rule-based extraction (teal) achieves $H \approx 1.0$ for adversative and hedging, while LLM-based extraction (coral) captures epistemic, lexical, and structural ambiguity. (B) Number of interpretations extracted per category. (C) Overall comparison: baseline systems collapse to $H = 0$, while $\phi$ preserves $H = 1.087$ across all 68 sentences.

Theorems & Definitions (12)

  • Definition 1: Text Space
  • Definition 2: Semantic State Space
  • Definition 3: Interpretation
  • Definition 4: Text-to-State Mapping
  • Definition 5: Conflict Markers
  • Definition 6: Conflict Detection Function
  • Definition 7: Hybrid Extraction
  • Definition 8: State Construction
  • Definition 9: State Entropy
  • Theorem 1: Non-Collapse of $\phi$
  • ...and 2 more