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)

Artificial Intelligence (AI) has advanced significantly, yet it faces challenges related to transparency, interpretability, and alignment with human cognition and ethics. Traditional mathematical frameworks underpinning AI often emphasize abstraction and formalism, leading to "blackbox" models that are difficult for humans to understand. This report introduces the DIKWP Semantic Mathematics, proposed by Prof. Yucong Duan, as a new mathematical framework tailored for AI. The DIKWP model integrates Data, Information, Knowledge, Wisdom, and Purpose, embedding semantics and human cognitive processes into mathematical constructs. This approach aims to transform AI systems from opaque semantic machines into transparent, conceptually aligned systems that mirror human understanding, thereby addressing the transparency problem and enhancing collaboration between humans and AI.

1. Introduction

• 1.1 Background and Motivation

• 1.2 Limitations of Traditional Mathematics in AI

• 1.3 Objectives of the Report

2. The DIKWP Semantic Mathematics Framework

• 2.2.1 Phenomenology

• 2.2.2 Constructivism

• 2.2.3 Semiotics

• 2.2.4 Ethics and Responsibility

• 2.1 Overview of the DIKWP Model

• 2.2 Philosophical Foundations

3. Detailed Construction of DIKWP Components

• 3.5.1 Mathematical Formalism

• 3.5.2 Goal Alignment in AI

• 3.4.1 Mathematical Formalism

• 3.4.2 Ethical Decision-Making in AI

• 3.3.1 Mathematical Formalism

• 3.3.2 Knowledge Representation in AI

• 3.2.1 Mathematical Formalism

• 3.2.2 Processing in AI

• 3.1.1 Mathematical Formalism

• 3.1.2 Integration in AI Systems

• 3.1 Data (D)

• 3.2 Information (I)

• 3.3 Knowledge (K)

• 3.4 Wisdom (W)

• 3.5 Purpose (P)

4. Addressing the Transparency Problem in AI

• 4.1 From Blackbox Models to Transparent Systems

• 4.2 Aligning AI with Human Conceptual Understanding

• 4.3 Enhancing Interpretability through DIKWP

5. Mathematical Foundations and Formalism

• 5.1 Semantic Representation of Data and Information

• 5.2 Construction of Knowledge Networks

• 5.3 Wisdom Function and Optimization

• 5.4 Purpose-Driven Transformations

6. Case Studies and Applications

• 6.1 Explainable AI in Healthcare

• 6.2 Autonomous Systems and Ethical Decision-Making

• 6.3 Natural Language Understanding and Generation

7. Benefits and Implications for AI Development

• 7.1 Improved Transparency and Trust

• 7.2 Ethical Alignment and Responsibility

• 7.3 Advancements in Human-AI Interaction

8. Challenges and Future Directions

• 8.1 Implementation Complexity

• 8.2 Balancing Performance and Interpretability

• 8.3 Standardization and Scalability

• 8.4 Interdisciplinary Collaboration

9. Conclusion

10. References

Artificial Intelligence has become integral to numerous aspects of modern life, from healthcare and finance to transportation and communication. Despite its advancements, AI faces critical challenges, particularly regarding transparency and interpretability. Traditional AI models, especially deep learning networks, often function as "blackbox" systems, processing data in ways that are not readily understandable to humans.

This lack of transparency hinders trust, limits collaboration, and raises ethical concerns. As AI systems become more autonomous and influential, ensuring that they are interpretable and aligned with human values is paramount. Prof. Yucong Duan's DIKWP Semantic Mathematics proposes a new mathematical framework that addresses these issues by integrating semantics and human cognitive processes into AI's mathematical foundations.

Traditional mathematics emphasizes abstraction, formalism, and objectivity. While these characteristics have driven scientific progress, they also contribute to the opacity of AI models:

• Abstraction from Semantics: Mathematical models often detach from real-world meanings, making it difficult to interpret results in a human-understandable way.

• Exclusion of Human Cognition: Traditional approaches may neglect the role of human cognitive processes, leading to AI systems that do not align with human reasoning.

• Ethical Considerations: Ethics are typically external to mathematical models, which can result in AI systems that do not account for human values.

This report aims to:

• Introduce the DIKWP Semantic Mathematics framework and its components.

• Detail the mathematical formalism of each component and their integration into AI systems.

• Explain how DIKWP addresses the transparency problem in AI.

• Provide case studies demonstrating practical applications.

• Discuss the benefits, challenges, and future directions of adopting DIKWP in AI development.

The DIKWP model extends the traditional Data-Information-Knowledge-Wisdom (DIKW) hierarchy by incorporating Purpose (P) as a fundamental component. Each level represents a stage in the cognitive processing of information, integrating semantics and human cognition:

1. Data (D): Specific instances with shared semantic attributes.

2. Information (I): Data processed to highlight meaningful differences, guided by purpose.

3. Knowledge (K): Structured understanding through relationships and abstractions.

4. Wisdom (W): Integration of ethics and values into decision-making.

5. Purpose (P): Goal-oriented direction guiding cognitive processes.

• Core Idea: Emphasizes lived experiences and intentionality.

• Application in DIKWP: Grounds mathematical constructs in human experiences, ensuring that AI models reflect how humans perceive and interpret information.

• Core Idea: Knowledge is actively constructed by the knower through cognitive processes.

• Application in DIKWP: Encourages the development of AI systems that build knowledge structures similar to human conceptual frameworks.

• Core Idea: Studies signs and symbols as essential components of communication and meaning.

• Application in DIKWP: Ensures that data and information in AI systems carry semantic meanings understandable by humans.

• Core Idea: Integrates ethical considerations into decision-making processes.

• Application in DIKWP: Embeds ethics into the wisdom component, aligning AI actions with human values and societal norms.

Definition: Data represents specific instances or observations that share common semantic attributes within the cognitive framework of an entity.

Let:

• $S$ be a set of shared semantic attributes:

  S={f1,f2,…,fn}S = \{ f_1, f_2, \dots, f_n \}S={f1​,f2​,…,fn​}

• $D$ be the set of data instances $d$ such that:

  $$D=\{d\mid \text{Attributes}(d)\supseteq S\}$$

Interpretation: Data instances are grouped into concepts based on shared attributes, reflecting semantic categorization rather than purely syntactic grouping.

• Semantic Data Representation: AI systems annotate data with semantic metadata, making it more informative and interpretable.

• Example: In image recognition, pixels are associated with semantic labels (e.g., edges, textures) to form meaningful data constructs.

Definition: Information arises when differences in semantics are recognized and interpreted, guided by a specific purpose.

Define the information processing function FIF_IFI​:

FI:X×P→YF_I: X \times P \rightarrow YFI​:X×P→Y

Where:

• X={S1,S2,…,Sm}X = \{ S_1, S_2, \dots, S_m \}X={S1​,S2​,…,Sm​} is the set of input semantic configurations.

• $P$ represents the purpose guiding the interpretation.

• $Y$ is the set of output semantic associations or insights.

Interpretation: FIF_IFI​ transforms input semantics $X$ into new information $Y$ by highlighting meaningful differences relevant to the purpose $P$.

• Contextual Analysis: AI systems process data in context, considering the purpose to generate relevant information.

• Example: In natural language processing, recognizing the sentiment in text requires interpreting words within the context of a sentence, guided by the purpose of sentiment analysis.

Definition: Knowledge represents structured, abstracted, and generalized understandings, forming a cohesive semantic network.

Let:

• $K=(N,E)$ be a knowledge graph, where:

• N={n1,n2,…,nk}N = \{ n_1, n_2, \dots, n_k \}N={n1​,n2​,…,nk​} is the set of concept nodes.

• E={e1,e2,…,em}E = \{ e_1, e_2, \dots, e_m \}E={e1​,e2​,…,em​} is the set of edges representing relationships.

An edge $e$ between nodes nin_ini​ and njn_jnj​ with relationship $r$:

e=(ni,nj,r)e = (n_i, n_j, r)e=(ni​,nj​,r)

Interpretation: Knowledge is structured as a network where concepts are connected through meaningful relationships.

• Conceptual Models: AI systems build knowledge graphs to represent relationships between concepts.

• Example: In recommendation systems, products are linked based on user behavior and preferences, forming a knowledge network.

Definition: Wisdom involves the ethical and value-laden processing of knowledge, information, and data, guided by purpose, resulting in optimized and holistic outcomes.

Define the wisdom function $W$:

W:{D,I,K,Wprev,P}→{D∗,I∗,K∗,Wpost,P∗}W: \{ D, I, K, W_{\text{prev}}, P \} \rightarrow \{ D^*, I^*, K^*, W_{\text{post}}, P^* \}W:{D,I,K,Wprev​,P}→{D∗,I∗,K∗,Wpost​,P∗}

Where:

• D∗,I∗,K∗,P∗D^*, I^*, K^*, P^*D∗,I∗,K∗,P∗ are the optimized components after applying wisdom.

• WprevW_{\text{prev}}Wprev​ is the prior wisdom or ethical framework.

• WpostW_{\text{post}}Wpost​ is the updated wisdom incorporating new insights.

Interpretation: Wisdom enhances all DIKWP components by integrating ethical considerations and higher-order thinking.

• Ethical Frameworks: AI systems incorporate ethics into their decision-making processes.

• Example: In autonomous vehicles, ethical algorithms determine actions in scenarios involving potential harm, aligning decisions with societal values.

Definition: Purpose provides intentionality and goal-directedness, guiding the processing of data, information, knowledge, and wisdom.

Define purpose $P$:

$$P=(\text{Goals},\text{Constraints},\text{Values})$$

Transformation function guided by purpose:

TP:{D,I,K}→{D∗,I∗,K∗}T_P: \{ D, I, K \} \rightarrow \{ D^*, I^*, K^* \}TP​:{D,I,K}→{D∗,I∗,K∗}

Interpretation: Purpose shapes how data, information, and knowledge are processed and transformed, ensuring alignment with goals and values.

• Objective Setting: AI systems define objectives that guide their operations.

• Example: In personalized education platforms, the purpose is to optimize learning outcomes for individual students, guiding content delivery and assessments.

Traditional AI models often lack interpretability due to:

• Complexity: High-dimensional spaces and nonlinear transformations.

• Opacity: Lack of accessible explanations for internal processes.

DIKWP Solution:

• Semantic Integration: Embeds meaning into data and processes, making them more interpretable.

• Structured Knowledge: Constructs knowledge graphs that are understandable and can be visualized.

• Ethical Alignment: Decisions are made transparently, considering ethical frameworks.

By mirroring human cognitive structures:

• Conceptual Alignment: AI systems process information similarly to humans, facilitating understanding.

• Communication: Outputs can be explained in terms that humans comprehend.

• Example: An AI diagnosing medical conditions explains its reasoning using medical concepts familiar to healthcare professionals.

• Transparent Decision Paths: Wisdom and purpose guide decision-making in ways that can be traced and explained.

• Semantic Processing: Information and knowledge are processed with semantic awareness, making intermediate steps interpretable.

• Visualization: Knowledge graphs and conceptual maps can be visualized, aiding understanding.

• Data Structures: Utilize data models that include semantic annotations.

• Mathematical Representation:

  For a data instance $d$:

  d={(fi,vi)∣fi∈S,vi∈V}d = \{ (f_i, v_i) \mid f_i \in S, v_i \in V \}d={(fi​,vi​)∣fi​∈S,vi​∈V}

  Where fif_ifi​ is a semantic feature, and viv_ivi​ is its value.

• Information Processing Functions: Designed to maintain and enhance semantic content.

• Nodes and Edges: Represent concepts and relationships with clear semantic meanings.

• Mathematical Representation:

  Knowledge graph $K=(N,E)$ with:

• Nodes N={ni}N = \{ n_i \}N={ni​} representing concepts.

• Edges E={(ni,nj,rij)}E = \{ (n_i, n_j, r_{ij}) \}E={(ni​,nj​,rij​)} representing relationships rijr_{ij}rij​.

• Operations on Knowledge Graphs:

• Addition of Nodes/Edges: Incorporate new knowledge.

• Traversal: Explore relationships to derive insights.

• Mathematical Representation:

  W:{D,I,K,Wprev,P}→{D∗,I∗,K∗,Wpost,P∗}W: \{ D, I, K, W_{\text{prev}}, P \} \rightarrow \{ D^*, I^*, K^*, W_{\text{post}}, P^* \}W:{D,I,K,Wprev​,P}→{D∗,I∗,K∗,Wpost​,P∗}

• Optimization Process:

• Objective Function: Defined by ethical considerations and purpose.

• Constraints: Reflect ethical boundaries and values.

• Solution Methods: Utilize optimization algorithms that account for both performance and ethical factors.

• Transformation Function:

  TP:{D,I,K}→{D∗,I∗,K∗}T_P: \{ D, I, K \} \rightarrow \{ D^*, I^*, K^* \}TP​:{D,I,K}→{D∗,I∗,K∗}

• Mathematical Formalism:

• Purpose $P$: Encoded as a set of goals $G$, constraints $C$, and values $V$.

• Transformation Rules: Derived from $P$, guiding the processing of $D$, $I$, and $K$.

Scenario:

An AI system provides diagnoses and treatment recommendations. Transparency is crucial for trust and compliance with regulations.

Application of DIKWP:

• Data (D): Patient records with semantic annotations (symptoms, test results).

• Information (I): Processes data to identify significant medical indicators.

• Knowledge (K): Constructs knowledge graphs linking symptoms, diseases, treatments.

• Wisdom (W): Considers ethical principles like patient privacy and informed consent.

• Purpose (P): Aims to improve patient outcomes through accurate, understandable recommendations.

Outcome:

• Transparency: The AI can explain its reasoning in medical terms.

• Trust: Healthcare professionals understand and trust the AI's decisions.

• Compliance: Meets legal requirements for explainability.

Scenario:

An autonomous vehicle must make split-second decisions in complex environments, requiring ethical considerations.

Application of DIKWP:

• Data (D): Sensor inputs labeled with semantic context (pedestrians, obstacles).

• Information (I): Identifies potential hazards and their significance.

• Knowledge (K): Maintains situational awareness maps.

• Wisdom (W): Applies ethical frameworks to prioritize actions (e.g., minimizing harm).

• Purpose (P): Ensures safety and compliance with traffic laws.

Outcome:

• Transparency: Decision-making processes are explainable.

• Ethical Alignment: Actions reflect societal values.

• Safety: Improved decision-making leads to safer outcomes.

Scenario:

An AI language model generates responses in conversational agents. Transparency and coherence are essential.

Application of DIKWP:

• Data (D): Text data with semantic annotations (topics, sentiments).

• Information (I): Processes language structures contextually.

• Knowledge (K): Builds conceptual understanding of language and topics.

• Wisdom (W): Avoids generating inappropriate or biased content.

• Purpose (P): Provides meaningful and coherent communication.

Outcome:

• Interpretability: Responses are grounded in conceptual understanding.

• Quality: Improved coherence and relevance.

• Ethical Standards: Communication aligns with ethical guidelines.

• Interpretability: Systems are designed to be understandable by humans.

• Accountability: Transparent processes facilitate error detection and correction.

• Value Integration: AI actions reflect human values and societal norms.

• Regulatory Compliance: Meets legal requirements for explainability and ethical standards.

• Collaboration: Enhanced understanding enables better cooperation between humans and AI.

• User Acceptance: Transparent and ethical AI systems are more likely to be accepted and adopted.

• Technical Challenges: Integrating semantics and ethics into AI models requires advanced methodologies.

• Resource Demands: May increase computational and development resources needed.

• Trade-offs: Enhancing transparency may impact system performance.

• Optimization: Research needed to find optimal balances.

• Consistency: Developing standardized approaches for semantic integration.

• Scalability: Ensuring methods can be applied across various AI applications.

• Expertise Integration: Combining knowledge from mathematics, philosophy, cognitive science, and AI.

• Future Research: Encouraging interdisciplinary projects to advance DIKWP adoption.

The DIKWP Semantic Mathematics presents a transformative approach to AI development, addressing the transparency problem by integrating semantics, human cognition, and ethics into mathematical frameworks. By aligning AI systems with human conceptual understanding, DIKWP enables the creation of AI models that are transparent, interpretable, and ethically aligned. While challenges exist in implementation and optimization, the potential benefits for trust, collaboration, and responsible AI development are significant. Embracing DIKWP Semantic Mathematics can lead to AI systems that not only perform effectively but also resonate with human values and understanding, fostering a more harmonious integration of AI into society.

• Brouwer, L.E.J. Intuitionism and Formalism.

• Duan, Y. Proposals on DIKWP Semantic Mathematics.

• Heidegger, M. Being and Time.

• Husserl, E. Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy.

• Jonas, H. The Imperative of Responsibility.

• Peirce, C.S. Collected Papers.

• Whitehead, A.N. Process and Reality.

• Relevant literature on AI transparency, explainable AI, and ethical AI development.

Note: This technical report provides a detailed exploration of the DIKWP Semantic Mathematics as a new mathematical framework for AI. It focuses on how DIKWP addresses the transparency problem by transforming AI systems into transparent, conceptually aligned systems that humans can understand and trust. The report includes mathematical formalism, philosophical foundations, practical applications, and discussions on benefits and challenges, offering a comprehensive view of DIKWP's potential impact on AI development.