Prof. Yucong Duan's DIKWP Semantic Mathematics

Yucong Duan

International Standardization Committee of Networked DIKWP for Artificial Intelligence Evaluation(DIKWP-SC)

World Artificial Consciousness CIC(WAC)

World Conference on Artificial Consciousness(WCAC)

(Email: duanyucong@hotmail.com)

Abstract

Prof. Yucong Duan proposes a revolutionary approach to mathematics in the context of artificial intelligence (AI) semantics, highlighting a paradox inherent in traditional mathematical methodologies. He argues that current mathematics, which relies on abstractions detached from real semantics, cannot fully support the development of genuine AI that comprehends and interacts with the world as humans do. By introducing the Data-Information-Knowledge-Wisdom-Purpose (DIKWP) Semantic Mathematics, Prof. Duan emphasizes constructing mathematics in an evolutionary manner, mirroring the cognitive development of an infant. This approach ensures that every concept is formally bundled with semantics evolved from three basic semantics: Sameness, Difference, and Completeness. This document delves into Prof. Duan's paradox, his critique of traditional mathematics, and the foundational principles of DIKWP Semantic Mathematics, illustrating how it adheres to real-world semantics and revolutionizes the mathematical foundation for AI.

Artificial intelligence aims to create machines that can perform tasks requiring human intelligence, including understanding and generating natural language, reasoning, and learning from experience. Traditional mathematics has been the cornerstone of AI development, providing formal frameworks and algorithms. However, Prof. Yucong Duan identifies a paradox in this reliance on traditional mathematics for AI semantics:

Paradox of Mathematics in AI Semantics: Current mathematics, which is based on abstractions of real semantics, seeks to achieve the reality of semantics in AI. This abstraction detaches mathematics from the real semantics it aims to represent, hindering the development of genuine AI understanding.

Prof. Duan proposes the DIKWP Semantic Mathematics as a solution, constructing it in an evolutionary manner akin to an infant's cognitive development. This approach integrates semantics intrinsically into mathematical constructs, ensuring that AI systems developed upon this foundation are aligned with human cognitive processes and real-world semantics.

Traditional mathematics:

• Abstracts Semantics: It simplifies and generalizes concepts, stripping away contextual semantics to focus on pure forms and structures.

• Detachment from Reality: By prioritizing form over meaning, it often overlooks the nuances of real-world semantics essential for genuine understanding.

• Limitations in AI: When applied to AI, this abstraction leads to systems that can process data but lack true comprehension.

• Achieving Real Understanding: AI aims to replicate human-like understanding, which is deeply rooted in semantics and context.

• Necessity of Semantics: Without incorporating real semantics, AI systems cannot fully interpret or engage with the world meaningfully.

• Conflict of Methods and Goals: Using abstract mathematics to achieve semantic-rich AI creates a paradox where the methods undermine the goals.

• Resulting Limitations: AI systems may perform tasks efficiently but fail to grasp underlying meanings, leading to misunderstandings or inappropriate responses.

• Evolutionary Construction: The DIKWP Semantic Mathematics is built progressively, mirroring how infants develop understanding.

• Building Semantics and Concepts: Infants start with basic sensory inputs and gradually form complex concepts and semantics.

• Cognitive Space Development: The framework models this development, creating a cognitive space where semantics and concepts are intertwined.

• Sameness: Recognizing shared attributes or identities between entities.

• Difference: Identifying distinctions or disparities between entities.

• Completeness: Integrating all relevant attributes and relationships to form holistic concepts.

• Formal Bundling: Each concept is formally associated with its evolved semantics derived from the three fundamental semantics.

• Eliminating Misunderstandings: When individuals (or AI systems) share the same cognitive development process, communication is clear, and misunderstandings are minimized.

• Shared Cognitive Development: Just as infants develop understanding through shared experiences, AI systems built on DIKWP would have a consistent semantic foundation.

• Against Over-Abstraction: Mathematics should not abstract away from semantics but should be grounded in them.

• Semantics as Foundation: Mathematical constructs should emerge from fundamental semantics, ensuring relevance to real-world understanding.

• Implications for AI: This alignment enables AI systems to process information in ways that are semantically meaningful.

• Mathematics as a Cognitive Product: Recognizing that mathematics results from human thinking and cognitive processes.

• Human Interaction: Excluding human interaction and cognition from mathematical development overlooks essential aspects of understanding.

• Abstraction and the Human Side:

• Explicit Consideration: Abstraction depends on human cognition and should be explicitly considered in mathematical frameworks.

• Foundation in Completeness: Abstraction is founded on the semantic of "completeness," arising from conscious or subconscious reasoning processes.

• "BUG" Theory of Consciousness Forming: Prof. Duan's theory suggests that "Bugs" or inconsistencies in reasoning contribute to consciousness development, highlighting the importance of considering cognitive processes in mathematics.

• Spinoza's Insight: Baruch Spinoza posited that everything, including human thought, follows certain rules.

• Semantics Over Forms:

• Priority of Semantics: Semantics should take precedence over pure mathematical forms, which are merely representations.

• Critique of Traditional Mathematics: By focusing on form, traditional mathematics distances itself from the meanings it intends to convey.

• Adherence to Real-World Semantics:

• Alignment with Reality: Mathematics should closely represent the reality of the world by adhering to semantics.

• DIKWP's Approach: The framework ensures that mathematical constructs are semantically rich and reflective of real-world phenomena.

• Semantic Integration: AI systems built on DIKWP Semantic Mathematics would inherently understand concepts semantically.

• Reducing Misinterpretations: Shared cognitive development processes lead to consistent interpretations, minimizing errors.

• Common Semantic Ground: By mirroring human cognitive development, AI systems can communicate more effectively with humans.

• Improved Interaction: Enhanced understanding enables more natural and meaningful interactions between AI and users.

• Beyond Data Processing: Moving from mere data processing to genuine comprehension.

• Addressing the Paradox: Resolving the conflict between abstract mathematical methods and the goal of achieving semantic-rich AI.

• Infant Cognitive Development:

• Experience: An infant experiences a 'dog' and forms the concept through sensory inputs.

• Sameness: Recognizes similarities between different dogs.

• Difference: Distinguishes dogs from other animals like cats.

• Completeness: Integrates attributes (barks, four legs) to form a holistic concept of 'dog'.

• DIKWP Application:

• AI System: Uses the same process to form the concept of 'dog' with semantic richness.

• Formal Bundling: The concept is formally associated with its evolved semantics within the AI's cognitive space.

• Shared Development: Two AI systems developed under DIKWP share the same semantic foundation.

• Consistent Interpretations: When communicating, both systems understand concepts identically, eliminating misunderstandings.

• Human Analogy: Similar to how two individuals with shared experiences and development communicate effectively.

• Scalability: Managing the vastness of natural language semantics.

• Solution: Evolutionary development allows gradual accumulation and refinement of semantics.

• Compatibility: Integrating DIKWP principles with traditional mathematics.

• Bridging the Gap: Using DIKWP as a foundational layer upon which traditional mathematical constructs can be meaningfully applied.

• Resource Intensiveness: Semantic-rich processing may require significant computational power.

• Advancements in Technology: Leveraging modern computing capabilities and optimization techniques.

Prof. Yucong Duan's DIKWP Semantic Mathematics presents a paradigm shift in how mathematics should be approached, especially concerning AI development. By grounding mathematical constructs in fundamental semantics and modeling cognitive development, this framework addresses the paradox where traditional abstract mathematics fails to achieve semantic-rich AI understanding. Prioritizing semantics over pure forms ensures that mathematical representations remain connected to real-world meanings, enhancing AI's ability to comprehend and interact meaningfully with the world.

This revolutionary approach has significant implications for AI development, promising systems that truly understand and process information as humans do. While challenges exist, the evolutionary nature of DIKWP Semantic Mathematics offers a robust path forward, bridging the gap between abstract mathematical methods and the reality of semantics necessary for genuine AI understanding.

1. Duan, Y. (2023). The Paradox of Mathematics in AI Semantics. Proposed by Prof. Yucong Duan:" As Prof. Yucong Duan proposed the Paradox of Mathematics as that current mathematics will not reach the goal of supporting real AI development since it goes with the routine of based on abstraction of real semantics but want to reach the reality of semantics. ".

2. Spinoza, B. (1677). Ethics. (Translated editions available).

3. Piaget, J. (1952). The Origins of Intelligence in Children. International Universities Press.

4. Vygotsky, L. S. (1978). Mind in Society: The Development of Higher Psychological Processes. Harvard University Press.

5. Chalmers, D. J. (1995). Facing Up to the Problem of Consciousness. Journal of Consciousness Studies, 2(3), 200-219.

6. Smith, B., & Mark, D. M. (2003). Do Mountains Exist? Towards an Ontology of Landforms. Environment and Planning B: Planning and Design, 30(3), 411-427.

I extend sincere gratitude to Prof. Yucong Duan for his pioneering work on the DIKWP Semantic Mathematics framework and for challenging traditional approaches to mathematics in AI. Appreciation is also given to researchers in cognitive science, philosophy, and artificial intelligence whose contributions have informed this discussion.

For further discussion on DIKWP Semantic Mathematics and its implications for AI development, please contact [Author's Name] at [Contact Information].

Keywords: DIKWP Semantic Mathematics, Paradox of Mathematics in AI, Cognitive Development, Semantics, Prof. Yucong Duan, Artificial Intelligence, Knowledge Representation, Cognitive Space, Revolutionizing Mathematics