Bridging Cognitive and Expression Spaces in Creative AI by Integrating DIKWP-TRIZ and Semantic Mathematics

Large Language Models (LLMs) generate fluent text but often struggle with reliable multi-step reasoning, factual grounding, and stable use of long context, especially when inputs are incomplete, inconsistent, or imprecise. To address these challenges, we propose a Creative AI framework that integrates DIKWP-TRIZ with a semantic-mathematical constraint layer. DIKWP-TRIZ extends TRIZ by embedding a DIKWP (Data–Information–Knowledge–Wisdom–Purpose) network, enabling purposeful, value-aware transformations and explicit repair operations under 3-No conditions. The semantic layer introduces three context-indexed constraints over concept–expression mappings (Existence, Contextual Uniqueness, and Transitivity), making ambiguities and contradictions explicit and checkable during inference and generation. We enumerate the DIKWP × DIKWP transformation type space (25 ordered pairs over {D,I,K,W,P}) and provide candidate TRIZ inventive principles for each type as design-time guidance. A global Purpose controller steers transformation selection and enforces goal alignment and ethical constraints. We present a reference architecture and qualitative case analyses against a standard LLM, illustrating how the framework structures intermediate steps, surfaces assumptions, and supports traceable explanations. Quantitative benchmarking remains for future work.