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Natural Language Processing (NLP) faces a critical disjunction: science-oriented AI relies on rigid formal logic but struggles to capture flexible linguistic semantics, while humanities-oriented AI leverages semantic intuition yet lacks a rigorous mathematical foundation. Meanwhile, traditional relational databases, constrained by fixed row-column structures, fail to represent hierarchical linguistic composition (e.g., stroke → radical → Chinese character) and dynamic semantic associations.To address these issues, this paper constructs a formal system for Smart System Studies, unifying language and databases through three core mechanisms: atomized decomposition of Meta-Atoms/Elements and Meta-Tuples, hierarchical modeling via bi-categories (for semantic layers) and fibred categories (for dynamic rule-instance binding), and fuzzy semantic processing using probabilistic functors. Key contributions include proposing the ‘‘indecomposable Meta-Atoms/Elements + free monoid Meta-Tuples’’ model (unifying character/language representation granularity) and verifying the system’s effectiveness across semantic search, Chinese-English cross-language translation and Chinese character Experiments show its categorical database outperforms MySQL and Neo4j by 35.2%–42.7% in semantic query accuracy and 38.1%–51.3% in response time reduction; in cross-language tasks, its semantic consistency (XSTS score) exceeds the Transformer baseline by 8.9%. This system provides a unified mathematical substrate to bridge science- and humanities-oriented AI, advancing human-computer collaboration from mechanical matching to semantic understanding.

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Formal System: A Category Theory-Based Unified Framework for Language-Databases and Cross-Modal Human-Computer Collaboration

  • 会议论文

  • 发表日期：

    2026年

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  • Shunpeng Zou,
  • Xiaohui Zou

摘要

Natural Language Processing (NLP) faces a critical disjunction: science-oriented AI relies on rigid formal logic but struggles to capture flexible linguistic semantics, while humanities-oriented AI leverages semantic intuition yet lacks a rigorous mathematical foundation. Meanwhile, traditional relational databases, constrained by fixed row-column structures, fail to represent hierarchical linguistic composition (e.g., stroke → radical → Chinese character) and dynamic semantic associations.To address these issues, this paper constructs a formal system for Smart System Studies, unifying language and databases through three core mechanisms: atomized decomposition of Meta-Atoms/Elements and Meta-Tuples, hierarchical modeling via bi-categories (for semantic layers) and fibred categories (for dynamic rule-instance binding), and fuzzy semantic processing using probabilistic functors. Key contributions include proposing the ‘‘indecomposable Meta-Atoms/Elements + free monoid Meta-Tuples’’ model (unifying character/language representation granularity) and verifying the system’s effectiveness across semantic search, Chinese-English cross-language translation and Chinese character Experiments show its categorical database outperforms MySQL and Neo4j by 35.2%–42.7% in semantic query accuracy and 38.1%–51.3% in response time reduction; in cross-language tasks, its semantic consistency (XSTS score) exceeds the Transformer baseline by 8.9%. This system provides a unified mathematical substrate to bridge science- and humanities-oriented AI, advancing human-computer collaboration from mechanical matching to semantic understanding.