Derivation of Semantics in 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

In the DIKWP Semantic Mathematics framework proposed by Prof. Yucong Duan, the semantics of Sameness, Difference, and Completeness are not static but are derived iteratively. When evaluating the Sameness between two Data or DIKWP concepts, we rely on the multiple existing Sameness semantics shared by the targeted concepts. This process allows for the derivation of multiple new Sameness semantics. The same iterative approach applies to the derivation of Difference and Completeness semantics. This document explores this iterative process, demonstrating how complex semantics are built upon existing identified closures of the three fundamental semantics, much like the cognitive development of an infant.

In the realm of Semantic Mathematics as envisioned by Prof. Yucong Duan, the semantics of Sameness, Difference, and Completeness serve as the foundational building blocks for modeling complex semantic structures. The key aspect of this approach is the iterative derivation of these semantics, where each evaluation relies on previously established semantics.

• Sameness: Derived by identifying shared existing Sameness semantics between concepts.

• Difference: Derived by recognizing existing Difference semantics between concepts.

• Completeness: Derived by assessing the completeness semantics based on the existing identified closures.

This iterative process reflects the natural way in which humans, especially infants, develop cognitively—by building upon what is already known to understand new concepts.

When evaluating the Sameness between two concepts (Concept A and Concept B), we examine the existing Sameness semantics that each concept shares with other concepts.

Example:

• Concept A shares Sameness semantics with Concept C and Concept D.

• Concept B also shares Sameness semantics with Concept C and Concept E.

Shared Sameness Semantics:

• Both Concept A and Concept B share Sameness with Concept C.

By identifying the shared Sameness semantics, we can derive new Sameness semantics between Concept A and Concept B.

• First Level Sameness: Based on shared Sameness with Concept C.

• Second Level Sameness: If Concept D and Concept E share Sameness semantics, this provides another Sameness connection between A and B.

Iterative Process:

1. Initial Evaluation: Identify direct shared Sameness semantics.

2. Expansion: Explore indirect Sameness through connections with other concepts.

3. Iteration: Repeat the process, incorporating newly derived Sameness semantics to find further commonalities.

Through iterative derivation, we can build a network of Sameness semantics that captures the nuanced relationships between concepts.

• Hierarchical Clustering: Concepts can be grouped into clusters based on levels of shared Sameness semantics.

• Semantic Layers: Each iteration adds a layer of semantic depth, refining the understanding of Sameness between concepts.

Similarly, when evaluating the Difference between two concepts, we rely on existing Difference semantics.

Example:

• Concept A differs from Concept F in certain attributes.

• Concept B also differs from Concept F but in different attributes.

Deriving Difference Semantics Between A and B:

• Shared Differences: The differences that both A and B have with F can highlight similarities between A and B.

• Unique Differences: Differences unique to A or B can be identified through comparison.

1. Identify Existing Differences: Between the target concepts and other related concepts.

2. Compare Differences: Analyze how the differences relate to each other.

3. Derive New Differences: Based on the comparisons, new Difference semantics are established.

Iteration Continues:

• By considering the differences with additional concepts, we can refine the Difference semantics between A and B.

An iterative approach allows us to build a comprehensive network of Difference semantics.

• Difference Mapping: Visual representation of how concepts differ from one another.

• Semantic Distance: Quantitative measure of the degree of difference, which can be updated iteratively.

Completeness semantics are concerned with the totality of attributes or relationships that define a concept.

Derivation Process:

• Existing Completeness: Each concept has an existing set of attributes that constitute its completeness.

• Comparative Analysis: By comparing the completeness of two concepts, we can identify overlapping and unique attributes.

1. Initial Completeness Evaluation: Assess the completeness semantics of each concept individually.

2. Integration: Combine the completeness semantics to see how they complement or supplement each other.

3. Iteration: Use the integrated completeness as a new baseline for further evaluation.

Resulting in:

• Enhanced Completeness: A more comprehensive understanding of each concept through the inclusion of shared and unique attributes.

• Refined Concepts: Concepts evolve as their completeness semantics are iteratively updated.

At the Data level, concepts are basic and share fundamental attributes.

• Iterative Sameness Evaluation:

• First Iteration: Identify basic shared attributes between Data concepts.

• Subsequent Iterations: Discover deeper similarities by considering shared attributes with other related Data concepts.

Information arises from recognizing differences between Data concepts.

• Iterative Difference Evaluation:

• First Iteration: Note obvious differences between concepts.

• Further Iterations: Uncover subtler differences by examining relationships with other concepts.

Knowledge is built by integrating Information to achieve Completeness.

• Iterative Completeness Evaluation:

• First Iteration: Form an initial understanding based on known attributes.

• Continual Refinement: As new Sameness and Difference semantics are derived, update the completeness of concepts.

• Recognition of Sameness: Infants recognize familiar objects by shared features.

• Detection of Difference: They notice when something doesn't match their existing understanding.

• Building Completeness: Over time, they integrate these observations to form complete concepts.

• Repetition: Through repeated exposure and comparison, infants refine their understanding.

• Expansion: Each new experience builds upon previous knowledge.

• Abstraction: They begin to form abstract concepts from concrete experiences.

• Flexibility: The model adapts as new information is introduced.

• Scalability: Can handle increasing complexity without needing new foundational semantics.

• Natural Learning: Mirrors the way humans learn and understand the world.

• Incremental Understanding: Knowledge is built step by step, reinforcing previous learning.

• Transparency: Each semantic derivation step is clear and traceable.

• Explainability: Easier to understand how AI systems reach conclusions.

Let S(A) represent the set of Sameness semantics for Concept A.

• Initial Sameness Set:

  S(0)(A)={initial attributes of A}S^{(0)}(A) = \{ \text{initial attributes of } A \}S(0)(A)={initial attributes of A}

• Iterative Sameness Derivation:

  S(n+1)(A,B)=S(n)(A)∩S(n)(B)S^{(n+1)}(A,B) = S^{(n)}(A) \cap S^{(n)}(B)S(n+1)(A,B)=S(n)(A)∩S(n)(B)

  Where S(n)(A,B)S^{(n)}(A,B)S(n)(A,B) represents the Sameness semantics between A and B at iteration $n+1$.

Let D(A) represent the set of Difference semantics for Concept A.

• Initial Difference Set:

  D(0)(A)={initial distinctions of A}D^{(0)}(A) = \{ \text{initial distinctions of } A \}D(0)(A)={initial distinctions of A}

• Iterative Difference Derivation:

  D(n+1)(A,B)=D(n)(A)∪D(n)(B)−S(n+1)(A,B)D^{(n+1)}(A,B) = D^{(n)}(A) \cup D^{(n)}(B) - S^{(n+1)}(A,B)D(n+1)(A,B)=D(n)(A)∪D(n)(B)−S(n+1)(A,B)

Let C(A) represent the completeness of Concept A.

• Initial Completeness:

  C(0)(A)=S(0)(A)∪D(0)(A)C^{(0)}(A) = S^{(0)}(A) \cup D^{(0)}(A)C(0)(A)=S(0)(A)∪D(0)(A)

• Iterative Completeness Derivation:

  C(n+1)(A)=C(n)(A)∪S(n+1)(A,B)∪D(n+1)(A,B)C^{(n+1)}(A) = C^{(n)}(A) \cup S^{(n+1)}(A,B) \cup D^{(n+1)}(A,B)C(n+1)(A)=C(n)(A)∪S(n+1)(A,B)∪D(n+1)(A,B)

At each iteration:

1. Update Sameness Semantics based on shared attributes discovered.

2. Update Difference Semantics based on new distinctions identified.

3. Refine Completeness by integrating the updated Sameness and Difference semantics.

• Dynamic Ontologies: AI can build and update ontologies iteratively, reflecting the evolving understanding of concepts.

• Semantic Networks: Concepts are interconnected through multiple layers of Sameness and Difference semantics.

• Incremental Learning: AI systems can learn new concepts by relating them to existing ones through iterative derivation.

• Adaptability: The system adapts to new information without restructuring the foundational semantics.

• Semantic Parsing: Understanding language by iteratively deriving semantics based on word relationships.

• Contextual Interpretation: Context can modify the Sameness and Difference semantics, allowing for nuanced understanding.

The iterative derivation of Sameness, Difference, and Completeness semantics, as proposed by Prof. Yucong Duan, offers a powerful method for modeling complex semantic structures within the DIKWP framework. By relying on shared existing semantics and iteratively building upon them, we can derive multiple new semantics without introducing additional foundational elements.

This approach not only aligns with the natural cognitive development observed in humans but also provides practical advantages for developing AI systems capable of sophisticated semantic understanding and reasoning. By mirroring the iterative learning processes of infants, AI can achieve a more human-like comprehension of concepts and relationships.

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 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. Piaget, J. (1954). The Construction of Reality in the Child. Basic Books.

3. Rumelhart, D. E., & McClelland, J. L. (1986). Parallel Distributed Processing: Explorations in the Microstructure of Cognition. MIT Press.

4. Harnad, S. (1990). The Symbol Grounding Problem. Physica D: Nonlinear Phenomena, 42(1-3), 335-346.

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

I extend sincere gratitude to Prof. Yucong Duan for his groundbreaking work on DIKWP Semantic Mathematics and for clarifying the iterative approach to semantic derivation. Appreciation is also given to colleagues in cognitive science and artificial intelligence for their valuable insights.

For further discussion on the iterative derivation of semantics in DIKWP Semantic Mathematics, please contact [Author's Name] at [Contact Information].

Keywords: DIKWP Model, Semantic Mathematics, Sameness, Difference, Completeness, Iterative Derivation, Prof. Yucong Duan, Artificial Intelligence, Cognitive Development, Semantic Modeling, Knowledge Representation