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

• URL: http://arxiv.org/abs/2601.19933v1
• Date: Mon, 12 Jan 2026 08:04:47 GMT
• Title: Text-to-State Mapping for Non-Resolution Reasoning: The Contradiction-Preservation Principle
• Authors: Kei Saito,
• Abstract summary: Non-Resolution Reasoning (NRR) provides a formal framework for maintaining semantic ambiguity rather than forcing premature interpretation collapse.<n>This paper introduces the text-to-state mapping function that transforms linguistic input into superposition states within the NRR framework.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• WavePhaseNet: A DFT-Based Method for Constructing Semantic Conceptual Hierarchy Structures (SCHS) [0.0]
  This paper reformulates Transformer/Attention mechanisms in Large Language Models.<n> Dimensionality Reduction GPT-4's 24,576-dimensional embedding space exhibits a 1/f spectral structure based on language self-similarity and Zipf's law.<n>Cohomological Consistency Control The reduced embedding space, constructed via cohomological regularization over overlapping local windows, allows defining a graph structure and cochain complex.
  arXiv  Detail & Related papers  (2026-02-16T03:07:41Z)
• Beyond Memorization: Testing LLM Reasoning on Unseen Theory of Computation Tasks [8.210112631285666]
  Large language models (LLMs) have demonstrated strong performance on formal language tasks.<n>We introduce a benchmark for deterministic finite automata (DFA) construction from regular languages.<n>We show that models achieve perfect accuracy on factual questions and 84-90% on seen tasks, but accuracy drops sharply on unseen problems.
  arXiv  Detail & Related papers  (2026-01-19T21:00:31Z)
• Non-Resolution Reasoning (NRR): A Computational Framework for Contextual Identity and Ambiguity Preservation [0.0]
  Current artificial intelligence systems exhibit a fundamental architectural limitation: they resolve ambiguity prematurely.<n>This premature semantic collapse stems from classical identity assumptions embedded in standard neural architectures.<n>We propose Non-Resolution Reasoning (NRR), a computational framework that treats ambiguity retention as a valid reasoning mode.
  arXiv  Detail & Related papers  (2025-12-15T16:14:32Z)
• Are Language Models Efficient Reasoners? A Perspective from Logic Programming [109.47572890883248]
  Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of human-like reasoning: efficiency.<n>We propose a framework for assessing LM reasoning efficiency through the lens of logic programming.
  arXiv  Detail & Related papers  (2025-10-29T15:30:31Z)
• Step-Aware Policy Optimization for Reasoning in Diffusion Large Language Models [57.42778606399764]
  Diffusion language models (dLLMs) offer a promising, non-autoregressive paradigm for text generation.<n>Current reinforcement learning approaches often rely on sparse, outcome-based rewards.<n>We argue that this stems from a fundamental mismatch with the natural structure of reasoning.
  arXiv  Detail & Related papers  (2025-10-02T00:34:15Z)
• Implicit Reasoning in Large Language Models: A Comprehensive Survey [67.53966514728383]
  Large Language Models (LLMs) have demonstrated strong generalization across a wide range of tasks.<n>Recent studies have shifted attention from explicit chain-of-thought prompting toward implicit reasoning.<n>This survey introduces a taxonomy centered on execution paradigms, shifting the focus from representational forms to computational strategies.
  arXiv  Detail & Related papers  (2025-09-02T14:16:02Z)
• Large Language Models as Quasi-crystals: Coherence Without Repetition in Generative Text [0.0]
  essay proposes an analogy between large language models (LLMs) and quasicrystals, systems that exhibit global coherence without periodic repetition, generated through local constraints.<n> Drawing on the history of quasicrystals, it highlights an alternative mode of coherence in generative language: constraint-based organization without repetition or symbolic intent.<n>This essay aims to reframe the current discussion around large language models, not by rejecting existing methods, but by suggesting an additional axis of interpretation grounded in structure rather than semantics.
  arXiv  Detail & Related papers  (2025-04-16T11:27:47Z)
• Latent Lexical Projection in Large Language Models: A Novel Approach to Implicit Representation Refinement [0.0]
  Latent Lexical Projection (LLP) is introduced to refine lexical representations through a structured transformation into a latent space.<n>LLP integrates an optimized projection mechanism within an existing language model architecture.<n> Evaluations indicate a reduction in perplexity and an increase in BLEU scores, suggesting improvements in predictive accuracy and fluency.
  arXiv  Detail & Related papers  (2025-02-03T23:18:53Z)
• The Foundations of Tokenization: Statistical and Computational Concerns [51.370165245628975]
  Tokenization is a critical step in the NLP pipeline.<n>Despite its recognized importance as a standard representation method in NLP, the theoretical underpinnings of tokenization are not yet fully understood.<n>The present paper contributes to addressing this theoretical gap by proposing a unified formal framework for representing and analyzing tokenizer models.
  arXiv  Detail & Related papers  (2024-07-16T11:12:28Z)
• Prototype-based Aleatoric Uncertainty Quantification for Cross-modal Retrieval [139.21955930418815]
  Cross-modal Retrieval methods build similarity relations between vision and language modalities by jointly learning a common representation space. However, the predictions are often unreliable due to the Aleatoric uncertainty, which is induced by low-quality data, e.g., corrupt images, fast-paced videos, and non-detailed texts. We propose a novel Prototype-based Aleatoric Uncertainty Quantification (PAU) framework to provide trustworthy predictions by quantifying the uncertainty arisen from the inherent data ambiguity.
  arXiv  Detail & Related papers  (2023-09-29T09:41:19Z)
• Infusing Finetuning with Semantic Dependencies [62.37697048781823]
  We show that, unlike syntax, semantics is not brought to the surface by today's pretrained models. We then use convolutional graph encoders to explicitly incorporate semantic parses into task-specific finetuning.
  arXiv  Detail & Related papers  (2020-12-10T01:27:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.