Conversion of the Semantics of Data, Information, and Knowledge within the DIKWP*DIKWP Interaction Space

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

Within the Data-Information-Knowledge-Wisdom-Purpose (DIKWP) model, the seamless transformation and conversion of cognitive components—Data, Information, and Knowledge—are pivotal for effective human and artificial intelligence (AI) collaborations. This document delves into the conversion processes of the semantics of Data, Information, and Knowledge within the DIKWP*DIKWP interaction space. By elucidating the mathematical frameworks and providing detailed examples, we aim to offer a comprehensive understanding of how raw Data is transformed into structured Information and subsequently into actionable Knowledge. This exploration not only enhances the theoretical foundation of the DIKWP model but also provides practical insights for mitigating communication deficiencies such as the 3-No Problems—Incomplete Input/Output, Inconsistent Input/Output, and Imprecise Input/Output—within cognitive interactions.

The DIKWP model serves as a foundational framework for categorizing cognitive processes into five interconnected components: Data (D), Information (I), Knowledge (K), Wisdom (W), and Purpose (P). Effective collaboration between stakeholders, whether human or AI, relies heavily on the efficient conversion and integration of these components. Understanding the semantics—the meaning and interpretation—of Data, Information, and Knowledge, and how they interrelate through conversion processes, is essential for optimizing communication and decision-making.

This document focuses on the conversion of the semantics of Data, Information, and Knowledge within the DIKWP*DIKWP interaction space. We present mathematical representations of these conversions, supported by detailed examples that illustrate their practical applications and implications.

Before delving into the conversion processes, it is crucial to establish a clear understanding of the semantics associated with Data, Information, and Knowledge within the DIKWP model.

Definition:Data represents raw, unprocessed facts or observations. In the DIKWP model, Data embodies "sameness" through shared semantic attributes, allowing different instances to be categorized under the same concept based on these commonalities.

Semantic Attributes:

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

Where fif_ifi​ represents a semantic feature of the Data concept.

Mathematical Representation:

$$D=\{d\mid d\text{ shares }S\}$$

Definition:Information is processed Data that highlights patterns, relationships, and distinctions. It embodies "difference" by emphasizing varying semantic attributes, facilitating the identification of trends, anomalies, and correlations.

Semantic Attributes:

D={g1,g2,…,gm}D = \{g_1, g_2, \dots, g_m\}D={g1​,g2​,…,gm​}

Where gig_igi​ represents a semantic feature of the Information concept.

Mathematical Representation:

$$I=\{i\mid i\text{ encapsulates }D\}$$

Definition:Knowledge is the organized and contextualized Information that forms a coherent understanding of concepts. It embodies "completeness" by integrating comprehensive semantic attributes, enabling informed decision-making and problem-solving.

Semantic Attributes:

C={h1,h2,…,hk}C = \{h_1, h_2, \dots, h_k\}C={h1​,h2​,…,hk​}

Where hih_ihi​ represents a semantic feature of the Knowledge concept.

Mathematical Representation:

$$K=\{k\mid k\text{ encompasses }C\}$$

The conversion from Data to Information and subsequently to Knowledge involves systematic processing and transformation of semantic attributes. This section outlines the mathematical frameworks governing these conversions and provides illustrative examples.

Objective:Transform raw Data into meaningful Information by identifying patterns, relationships, and distinctions.

Mathematical Framework:

1. Data Aggregation:

   D={d1,d2,…,dn}\mathbf{D} = \{ d_1, d_2, \dots, d_n \}D={d1​,d2​,…,dn​}

   Aggregate Data instances sharing semantic attributes $S$.

2. Pattern Identification:Utilize statistical or machine learning techniques to detect patterns within the aggregated Data.

   $$\text{Patterns}=\text{IdentifyPatterns}(\mathbf{D})$$

3. Information Generation:Formulate Information by highlighting identified patterns and relationships.

   I={i1,i2,…,im}whereij=Patternj\mathbf{I} = \{ i_1, i_2, \dots, i_m \} \quad \text{where} \quad i_j = \text{Pattern}_jI={i1​,i2​,…,im​}whereij​=Patternj​

Example Scenario: Human-AI Collaborative Medical Diagnosis

Context:A human medical practitioner (Dr. Smith) collaborates with an AI diagnostic system (AI-Diagnosis) to diagnose a patient’s condition.

Data Collection:

DH={Age: 45,Symptoms: Cough, Fever, Shortness of Breath,Medical History: None}\mathbf{D}_H = \{\text{Age: 45}, \text{Symptoms: Cough, Fever, Shortness of Breath}, \text{Medical History: None}\}DH​={Age: 45,Symptoms: Cough, Fever, Shortness of Breath,Medical History: None}DA={Extensive medical datasets,Research articles on respiratory diseases}\mathbf{D}_A = \{\text{Extensive medical datasets}, \text{Research articles on respiratory diseases}\}DA​={Extensive medical datasets,Research articles on respiratory diseases}

Pattern Identification:AI-Diagnosis processes the Data to identify patterns associated with respiratory conditions.

Information Generation:

IA={Pattern: High likelihood of pneumonia based on symptoms and data trends}\mathbf{I}_A = \{\text{Pattern: High likelihood of pneumonia based on symptoms and data trends}\}IA​={Pattern: High likelihood of pneumonia based on symptoms and data trends}IH={Pattern: Moderate likelihood of bronchitis based on patient-specific factors}\mathbf{I}_H = \{\text{Pattern: Moderate likelihood of bronchitis based on patient-specific factors}\}IH​={Pattern: Moderate likelihood of bronchitis based on patient-specific factors}

Objective:Integrate and contextualize Information to form comprehensive Knowledge that supports informed decision-making.

Mathematical Framework:

1. Information Integration:Combine Information from multiple sources to build a cohesive understanding.

   Icombined=IA∪IB\mathbf{I}_{\text{combined}} = \mathbf{I}_A \cup \mathbf{I}_BIcombined​=IA​∪IB​

2. Contextualization:Embed Information within relevant contexts, considering factors such as historical data, environmental variables, and domain-specific knowledge.

   K=Contextualize(Icombined,Context)\mathbf{K} = \text{Contextualize}(\mathbf{I}_{\text{combined}}, \text{Context})K=Contextualize(Icombined​,Context)

3. Knowledge Structuring:Organize contextualized Information into structured Knowledge frameworks, such as ontologies or knowledge graphs.

   K={k1,k2,…,kp}wherekl=StructuredKnowledgel\mathbf{K} = \{ k_1, k_2, \dots, k_p \} \quad \text{where} \quad k_l = \text{StructuredKnowledge}_lK={k1​,k2​,…,kp​}wherekl​=StructuredKnowledgel​

Example Scenario: Human-AI Collaborative Medical Diagnosis

Information Integration:

Icombined={High likelihood of pneumonia,Moderate likelihood of bronchitis}\mathbf{I}_{\text{combined}} = \{\text{High likelihood of pneumonia}, \text{Moderate likelihood of bronchitis}\}Icombined​={High likelihood of pneumonia,Moderate likelihood of bronchitis}

Contextualization:Considering the patient’s lack of prior respiratory issues and the severity of symptoms.

Knowledge Structuring:

$$\mathbf{K}=\{\text{Comprehensive Diagnosis: Pneumonia is the more probable condition due to symptom severity and data trends}\}$$

To formalize the conversion processes, we employ mathematical models that quantify the transformation from Data to Information and from Information to Knowledge.

Assumptions:

• Data instances are represented as vectors in a high-dimensional semantic space.

• Patterns are detectable through clustering or classification algorithms.

Model:

1. Data Representation:

   D={d1,d2,…,dn}di∈Rm\mathbf{D} = \{ \mathbf{d}_1, \mathbf{d}_2, \dots, \mathbf{d}_n \} \quad \mathbf{d}_i \in \mathbb{R}^mD={d1​,d2​,…,dn​}di​∈Rm

2. Pattern Detection Function:

   Patterns=fpattern(D)\text{Patterns} = f_{\text{pattern}}(\mathbf{D})Patterns=fpattern​(D)

   Where fpatternf_{\text{pattern}}fpattern​ could be a clustering algorithm like K-Means or a classification algorithm like Decision Trees.

3. Information Formation:

   I={i1,i2,…,ik}ij=Patternj\mathbf{I} = \{ \mathbf{i}_1, \mathbf{i}_2, \dots, \mathbf{i}_k \} \quad \mathbf{i}_j = \text{Pattern}_jI={i1​,i2​,…,ik​}ij​=Patternj​

Assumptions:

• Information needs to be contextualized and integrated with existing Knowledge bases.

• Knowledge is represented in structured forms such as ontologies.

Model:

1. Information Integration:

   Icombined=I1∪I2∪⋯∪In\mathbf{I}_{\text{combined}} = \mathbf{I}_1 \cup \mathbf{I}_2 \cup \dots \cup \mathbf{I}_nIcombined​=I1​∪I2​∪⋯∪In​

2. Contextualization Function:

   K=fcontext(Icombined,Context)\mathbf{K} = f_{\text{context}}(\mathbf{I}_{\text{combined}}, \text{Context})K=fcontext​(Icombined​,Context)

   Where fcontextf_{\text{context}}fcontext​ incorporates domain-specific rules and contextual data.

3. Knowledge Structuring Function:

   K=fstructure(K)\mathbf{K} = f_{\text{structure}}(\mathbf{K})K=fstructure​(K)

   Where fstructuref_{\text{structure}}fstructure​ organizes the information into a structured Knowledge framework.

To illustrate the conversion processes, we present detailed examples across different DIKWP components within the interaction space.

Context:A human medical practitioner (Dr. Smith) collaborates with an AI diagnostic system (AI-Diagnosis) to diagnose a patient’s condition.

1. Data Collection:

   DH={Age: 45,Symptoms: Cough, Fever, Shortness of Breath,Medical History: None}\mathbf{D}_H = \{\text{Age: 45}, \text{Symptoms: Cough, Fever, Shortness of Breath}, \text{Medical History: None}\}DH​={Age: 45,Symptoms: Cough, Fever, Shortness of Breath,Medical History: None}DA={Extensive medical datasets,Research articles on respiratory diseases}\mathbf{D}_A = \{\text{Extensive medical datasets}, \text{Research articles on respiratory diseases}\}DA​={Extensive medical datasets,Research articles on respiratory diseases}

2. Pattern Identification:

• AI-Diagnosis processes DA\mathbf{D}_ADA​ to identify common patterns associated with respiratory conditions.

• Detects that persistent cough, fever, and shortness of breath are indicative of pneumonia in the absence of prior respiratory issues.

3. Information Generation:

   IA={High likelihood of pneumonia based on symptom severity and data trends}\mathbf{I}_A = \{\text{High likelihood of pneumonia based on symptom severity and data trends}\}IA​={High likelihood of pneumonia based on symptom severity and data trends}IH={Moderate likelihood of bronchitis based on patient-specific factors}\mathbf{I}_H = \{\text{Moderate likelihood of bronchitis based on patient-specific factors}\}IH​={Moderate likelihood of bronchitis based on patient-specific factors}

1. Information Integration:

   Icombined={High likelihood of pneumonia,Moderate likelihood of bronchitis}\mathbf{I}_{\text{combined}} = \{\text{High likelihood of pneumonia}, \text{Moderate likelihood of bronchitis}\}Icombined​={High likelihood of pneumonia,Moderate likelihood of bronchitis}

2. Contextualization:

• Considering patient’s lack of prior respiratory issues and the severity of current symptoms.

3. Knowledge Structuring:

   $$\mathbf{K}=\{\text{Comprehensive Diagnosis: Pneumonia is more probable due to symptom severity and lack of prior issues}\}$$

Impact:The conversion process transforms raw Data into actionable Knowledge, enabling Dr. Smith and AI-Diagnosis to converge on a more accurate diagnosis, enhancing patient care.

Context:A financial analyst (Ms. Johnson) collaborates with an AI forecasting system (AI-Forecast) to predict stock market trends.

1. Data Collection:

   DH={Current stock prices,Historical market data}\mathbf{D}_H = \{\text{Current stock prices}, \text{Historical market data}\}DH​={Current stock prices,Historical market data}DA={Extensive financial datasets,Economic indicators}\mathbf{D}_A = \{\text{Extensive financial datasets}, \text{Economic indicators}\}DA​={Extensive financial datasets,Economic indicators}

2. Pattern Identification:

• AI-Forecast analyzes DA\mathbf{D}_ADA​ to identify trends such as rising interest rates and geopolitical tensions affecting stock prices.

3. Information Generation:

   IA={Bearish trend due to rising interest rates and geopolitical tensions}\mathbf{I}_A = \{\text{Bearish trend due to rising interest rates and geopolitical tensions}\}IA​={Bearish trend due to rising interest rates and geopolitical tensions}IH={Bullish trend based on increasing GDP and low unemployment}\mathbf{I}_H = \{\text{Bullish trend based on increasing GDP and low unemployment}\}IH​={Bullish trend based on increasing GDP and low unemployment}

1. Information Integration:

   Icombined={Bearish trend,Bullish trend}\mathbf{I}_{\text{combined}} = \{\text{Bearish trend}, \text{Bullish trend}\}Icombined​={Bearish trend,Bullish trend}

2. Contextualization:

• Assessing the relative impact of rising interest rates versus economic growth indicators.

3. Knowledge Structuring:

   $$\mathbf{K}=\{\text{Balanced outlook: Market may experience volatility with potential for both bullish and bearish movements}\}$$

Impact:The conversion from conflicting Information to a balanced Knowledge framework allows Ms. Johnson and AI-Forecast to navigate market uncertainties more effectively, leading to informed investment strategies.

Context:A student (Alex) interacts with an AI tutoring system (AI-Tutor) to learn calculus.

1. Data Collection:

   DX={Student’s grades,Learning pace,Engagement metrics}\mathbf{D}_X = \{\text{Student's grades}, \text{Learning pace}, \text{Engagement metrics}\}DX​={Student’s grades,Learning pace,Engagement metrics}DA={Extensive calculus problems,Instructional content}\mathbf{D}_A = \{\text{Extensive calculus problems}, \text{Instructional content}\}DA​={Extensive calculus problems,Instructional content}

2. Pattern Identification:

• AI-Tutor analyzes Alex’s learning data to identify strengths and weaknesses in calculus topics.

3. Information Generation:

   IA={Strong understanding of derivatives, weak in integrals}\mathbf{I}_A = \{\text{Strong understanding of derivatives, weak in integrals}\}IA​={Strong understanding of derivatives, weak in integrals}IX={Prefers visual learning aids, struggles with abstract concepts}\mathbf{I}_X = \{\text{Prefers visual learning aids, struggles with abstract concepts}\}IX​={Prefers visual learning aids, struggles with abstract concepts}

1. Information Integration:

   Icombined={Strong in derivatives,Weak in integrals,Prefers visual aids,Struggles with abstract concepts}\mathbf{I}_{\text{combined}} = \{\text{Strong in derivatives}, \text{Weak in integrals}, \text{Prefers visual aids}, \text{Struggles with abstract concepts}\}Icombined​={Strong in derivatives,Weak in integrals,Prefers visual aids,Struggles with abstract concepts}

2. Contextualization:

• Considering Alex’s preference for visual aids to address struggles with abstract integral concepts.

3. Knowledge Structuring:

   $$\mathbf{K}=\{\text{Personalized learning path: Incorporate visual tools and step-by-step integral problem-solving techniques}\}$$

Impact:Through the conversion process, AI-Tutor provides Alex with tailored educational strategies, enhancing learning efficiency and academic performance in calculus.

To systematically enhance the conversion of Data to Information and Information to Knowledge, we employ mathematical optimization techniques that minimize deficiencies and maximize the effectiveness of the conversion.

The primary objective is to maximize the quality of Knowledge ($\mathcal{K}$) while minimizing the deficiencies in Data and Information ($\mathcal{D}$ and $\mathcal{I}$).

$$\max \mathcal{K}-\lambda \cdot (\mathcal{D}+\mathcal{I})$$

Where:

• $\mathcal{K}$: Quality measure of Knowledge.

• $\mathcal{D}$: Deficiency measure in Data.

• $\mathcal{I}$: Deficiency measure in Information.

• $\lambda$: Weighting factor balancing the importance of deficiency minimization against Knowledge quality maximization.

To ensure feasible and practical conversion processes, the following constraints are imposed:

1. Completeness Constraint:

   CX≥θC∀X∈{D,I,K}C_X \geq \theta_C \quad \forall X \in \{D, I, K\}CX​≥θC​∀X∈{D,I,K}

   Where θC\theta_CθC​ is the minimum acceptable completeness score.

2. Consistency Constraint:

   SX≥θS∀X∈{D,I,K}S_X \geq \theta_S \quad \forall X \in \{D, I, K\}SX​≥θS​∀X∈{D,I,K}

   Where θS\theta_SθS​ is the minimum acceptable consistency score.

3. Precision Constraint:

   PX≥θP∀X∈{D,I,K}P_X \geq \theta_P \quad \forall X \in \{D, I, K\}PX​≥θP​∀X∈{D,I,K}

   Where θP\theta_PθP​ is the minimum acceptable precision score.

Incorporate penalties for exceeding deficiency thresholds to enforce constraints.

Penalty=η⋅∑X∈{D,I,K}max⁡(0,(DX+IX)−θX)\text{Penalty} = \eta \cdot \sum_{X \in \{D, I, K\}} \max(0, (\mathcal{D}_X + \mathcal{I}_X) - \theta_X)Penalty=η⋅X∈{D,I,K}∑​max(0,(DX​+IX​)−θX​)

Where:

• $\eta$: Penalty coefficient.

• θX\theta_XθX​: Deficiency threshold for component $X$.

Integrate the penalty into the objective function to formulate the combined optimization problem.

$$\max \left(\mathcal{K}-\lambda \cdot (\mathcal{D}+\mathcal{I})-\text{Penalty}\right)$$

This formulation ensures that the conversion processes prioritize the enhancement of Knowledge quality while adhering to predefined deficiency constraints.

• Action: Gather DIKWP profiles from both stakeholders.

• Tools: Data aggregation systems, profiling algorithms.

• Action: Detect Incompleteness, Inconsistency, and Imprecision using predefined metrics.

• Tools: Gap analysis tools, similarity measures, entropy calculators.

• Action: Calculate completeness scores (CXC_XCX​), consistency scores (SXS_XSX​), and precision scores (PXP_XPX​).

• Tools: Mathematical computation frameworks (e.g., Python, MATLAB).

• Action: Develop targeted strategies based on identified and quantified problems.

• Tools: Decision support systems, optimization solvers.

• Action: Apply remediation strategies and continuously monitor their effectiveness.

• Tools: Feedback loops, iterative optimization processes.

The conversion of the semantics of Data, Information, and Knowledge within the DIKWP*DIKWP interaction space is a structured and systematic process essential for enhancing mutual understanding and collaboration between stakeholders. By employing mathematical frameworks and targeted remediation strategies, stakeholders can effectively transform raw Data into meaningful Information and comprehensive Knowledge, thereby mitigating communication deficiencies such as the 3-No Problems—Incomplete Input/Output, Inconsistent Input/Output, and Imprecise Input/Output.

This comprehensive approach not only strengthens the theoretical underpinnings of the DIKWP model but also provides practical methodologies for optimizing human-AI interactions across various domains, including medical diagnosis, financial forecasting, and educational tutoring.

Future Directions:

• Advanced Machine Learning Techniques: Integrate more sophisticated algorithms for pattern recognition and knowledge structuring.

• Real-Time Conversion Systems: Develop systems capable of real-time detection and remediation of the 3-No Problems.

• Empirical Validation: Conduct extensive studies to validate the effectiveness of the conversion frameworks in diverse real-world scenarios.

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The author extends gratitude to Prof. Yucong Duan for his pioneering work on the DIKWP model and the Theory of Relativity of Consciousness, which have significantly influenced the conceptual framework of this analysis. Appreciation is also given to colleagues in cognitive science and artificial intelligence for their invaluable feedback and insights.

Correspondence and requests for materials should be addressed to [Author's Name and Contact Information].

Keywords: DIKWP Model, Data-Information-Knowledge Conversion, Semantic Transformation, Human-AI Interaction, Cognitive Processing, 3-No Problems, Mathematical Framework, Knowledge Integration, Communication Deficiencies, Understanding Enhancement