Non-Resolution Reasoning (NRR): A Computational Framework for Contextual Identity and Ambiguity Preservation

Current artificial intelligence systems, despite remarkable capabilities in text generation and pattern recognition, exhibit a fundamental architectural limitation: they resolve ambiguity prematurely. This premature semantic collapse -- the tendency to collapse multiple valid interpretations into a single output -- stems from classical identity assumptions embedded in standard neural architectures. We propose Non-Resolution Reasoning (NRR), a computational framework that treats ambiguity retention as a valid reasoning mode rather than a defect to be eliminated. NRR introduces three core principles: (1) Non-Identity ($A \neq A$) -- the same symbol refers to different entities across contexts; (2) Approximate Identity ($A \approx A$) -- entities share partial structural overlap without being identical; and (3) Non-Resolution -- conflicting interpretations can coexist without forced convergence. We formalize these principles through three architectural components: Multi-Vector Embeddings for context-dependent representation, Non-Collapsing Attention for parallel interpretation retention, and Contextual Identity Tracking (CIT) for maintaining $A \neq A$ across inference. We demonstrate NRR's advantages through case studies in paradox handling, creative generation, and context-dependent reasoning. Crucially, we provide a minimal empirical validation on a synthetic context-shift task where an NRR-lite model achieves 90.9% out-of-distribution accuracy compared to 9.1% for standard architectures, demonstrating that ambiguity preservation enables structural generalization. NRR challenges the assumption that meaning must collapse to be useful, offering a foundation for AI systems capable of sophisticated ambiguity handling and creative reasoning. The question is not whether AI should resolve ambiguity, but when, how, and under whose control.