Conversion of the 3-No Problems 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

Effective communication within the Data-Information-Knowledge-Wisdom-Purpose (DIKWP) model is essential for seamless collaboration between stakeholders, whether human or artificial intelligence (AI) systems. The 3-No Problems—Incomplete Input/Output, Inconsistent Input/Output, and Imprecise Input/Output—are significant barriers that impede this communication. This document elucidates the conversion of these 3-No Problems within the DIKWP*DIKWP interaction space, detailing how these issues are identified, quantified, and transformed into actionable remediation strategies. Through mathematical frameworks and detailed examples, we demonstrate the practical application of converting the 3-No Problems to enhance mutual understanding and collaboration.

1. Introduction

The DIKWP model categorizes cognitive processes into five interconnected components: Data (D), Information (I), Knowledge (K), Wisdom (W), and Purpose (P). Effective interaction between two stakeholders (e.g., human and AI) within this framework requires the seamless exchange and integration of these components. However, the 3-No Problems—Incomplete Input/Output, Inconsistent Input/Output, and Imprecise Input/Output—can disrupt this process, leading to misunderstandings, errors, and inefficiencies.

Conversion of the 3-No Problems involves identifying these issues within the DIKWP*DIKWP interaction space, quantifying their extent, and applying systematic remediation strategies to mitigate their impact. This document provides a comprehensive guide on this conversion process, supported by mathematical models and illustrative examples.

2. Understanding the 3-No Problems in DIKWP*DIKWP Interaction Space2.1 Defining the 3-No Problems

1. Incomplete Input/Output (No-Incomplete): Occurs when one stakeholder lacks sufficient components (Data, Information, Knowledge, Wisdom, or Purpose) to fully comprehend or act upon the DIKWP elements being communicated by the other stakeholder.

2. Inconsistent Input/Output (No-Inconsistent): Arises when there are conflicting components between stakeholders, leading to confusion and misunderstanding.

3. Imprecise Input/Output (No-Imprecise): Happens when components exchanged are vague or ambiguous, undermining clarity and effective decision-making.

2.2 Mapping to DIKWP Components

While the 3-No Problems can predominantly affect specific DIKWP components, they are inherently cross-cutting issues that can impact any of the DIKWP components depending on the interaction context.

3. Conversion Framework for the 3-No Problems

The conversion of the 3-No Problems involves three primary stages:

1. Identification: Detecting the presence of Incompleteness, Inconsistency, or Imprecision within the DIKWP*DIKWP interaction space.

2. Quantification: Measuring the extent of these problems using mathematical metrics.

3. Remediation: Applying targeted strategies to address and mitigate the identified issues.

3.1 Identification of 3-No Problems

Incomplete Input/Output:

• Indicators: Missing data points, lack of necessary context, incomplete knowledge bases.

• Detection Methods: Comparative analysis of DIKWP components, gap analysis.

Inconsistent Input/Output:

• Indicators: Conflicting information, contradictory knowledge, misaligned purposes.

• Detection Methods: Consistency checks, similarity measures, conflict detection algorithms.

Imprecise Input/Output:

• Indicators: Vague descriptions, ambiguous terminology, lack of specificity.

• Detection Methods: Precision assessments, entropy measurements, clarity evaluations.

3.2 Quantification of 3-No Problems

Incomplete Input/Output (No-Incomplete):

• Completeness Score CXC_XCX​:

  CX=∣XA∩XB∣∣XA∪XB∣C_X = \frac{|\mathbf{X}_A \cap \mathbf{X}_B|}{|\mathbf{X}_A \cup \mathbf{X}_B|}CX​=∣XA​∪XB​∣∣XA​∩XB​∣​

  Where XA\mathbf{X}_AXA​ and XB\mathbf{X}_BXB​ are the DIKWP components from Stakeholder A and Stakeholder B, respectively.

• Gap Identification GXG_XGX​:

  GX=1−CXG_X = 1 - C_XGX​=1−CX​

Inconsistent Input/Output (No-Inconsistent):

• Consistency Score SXS_XSX​:

  SX=XA⋅XB∥XA∥∥XB∥S_X = \frac{\mathbf{X}_A \cdot \mathbf{X}_B}{\|\mathbf{X}_A\| \|\mathbf{X}_B\|}SX​=∥XA​∥∥XB​∥XA​⋅XB​​

• Inconsistency Measure IXI_XIX​:

  IX=1−SXI_X = 1 - S_XIX​=1−SX​

Imprecise Input/Output (No-Imprecise):

• Entropy-Based Precision Score PXP_XPX​:

  PX=1−HXHmaxP_X = 1 - \frac{H_X}{H_{\text{max}}}PX​=1−Hmax​HX​​

• Imprecision Measure MXM_XMX​:

  MX=1−PX=HXHmaxM_X = 1 - P_X = \frac{H_X}{H_{\text{max}}}MX​=1−PX​=Hmax​HX​​

  Where HXH_XHX​ is the Shannon entropy of the DIKWP component $X$, and HmaxH_{\text{max}}Hmax​ is the maximum possible entropy.

3.3 Remediation Strategies

Incomplete Input/Output (No-Incomplete):

• Strategy: Enhance data sharing, provide missing context, expand knowledge bases.

  Mathematical Representation:

  XB′=XB∪(XA−XB)\mathbf{X}_B' = \mathbf{X}_B \cup (\mathbf{X}_A - \mathbf{X}_B)XB′​=XB​∪(XA​−XB​)

Inconsistent Input/Output (No-Inconsistent):

• Strategy: Reconcile conflicting information, standardize data formats, align purposes.

  Mathematical Representation:

  XA′=XB′=XA+XB2\mathbf{X}_A' = \mathbf{X}_B' = \frac{\mathbf{X}_A + \mathbf{X}_B}{2}XA′​=XB′​=2XA​+XB​​

Imprecise Input/Output (No-Imprecise):

• Strategy: Clarify and specify terminology, provide detailed explanations, standardize communication protocols.

  Mathematical Representation:

  XA′=XA+ΔXA\mathbf{X}_A' = \mathbf{X}_A + \Delta \mathbf{X}_AXA′​=XA​+ΔXA​XB′=XB+ΔXB\mathbf{X}_B' = \mathbf{X}_B + \Delta \mathbf{X}_BXB′​=XB​+ΔXB​

4. Detailed Conversion Examples in DIKWP*DIKWP Interaction Space4.1 Example 1: 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.

4.1.1 Incomplete Input/Output

• Issue: AI-Diagnosis lacks specific patient Data provided by Dr. Smith.

• Detection:

  CD=∣DH∩DA∣∣DH∪DA∣=35=0.6C_D = \frac{|\mathbf{D}_H \cap \mathbf{D}_A|}{|\mathbf{D}_H \cup \mathbf{D}_A|} = \frac{3}{5} = 0.6CD​=∣DH​∪DA​∣∣DH​∩DA​∣​=53​=0.6

• Gap Identification:

  GD=1−CD=0.4G_D = 1 - C_D = 0.4GD​=1−CD​=0.4

• Remediation:

  Dr. Smith provides the missing Data to AI-Diagnosis.

  DA′=DA∪(DH−DA)=DA∪ΔDH\mathbf{D}_A' = \mathbf{D}_A \cup (\mathbf{D}_H - \mathbf{D}_A) = \mathbf{D}_A \cup \Delta \mathbf{D}_HDA′​=DA​∪(DH​−DA​)=DA​∪ΔDH​

• Updated Completeness Score:

  CD′=1.0(No incompleteness)C_D' = 1.0 \quad (\text{No incompleteness})CD′​=1.0(No incompleteness)

4.1.2 Inconsistent Input/Output

• Issue: Conflicting Information about patient symptoms.

• Detection:

  SI=IH⋅IA∥IH∥∥IA∥=0.2S_I = \frac{\mathbf{I}_H \cdot \mathbf{I}_A}{\|\mathbf{I}_H\| \|\mathbf{I}_A\|} = 0.2SI​=∥IH​∥∥IA​∥IH​⋅IA​​=0.2II=1−SI=0.8I_I = 1 - S_I = 0.8II​=1−SI​=0.8

• Remediation:

  Reconcile conflicting Information through dialogue or averaging.

  IA′=IB′=IH+IA2\mathbf{I}_A' = \mathbf{I}_B' = \frac{\mathbf{I}_H + \mathbf{I}_A}{2}IA′​=IB′​=2IH​+IA​​

4.1.3 Imprecise Input/Output

• Issue: Vague Knowledge about symptom severity.

• Detection:

  HK=1.5 bits,Hmax=2 bitsH_K = 1.5 \text{ bits}, \quad H_{\text{max}} = 2 \text{ bits}HK​=1.5 bits,Hmax​=2 bitsPK=0.25,MK=0.75P_K = 0.25, \quad M_K = 0.75PK​=0.25,MK​=0.75

• Remediation:

  Provide detailed semantic attributes for symptom severity.

  KA′=KA+ΔKA\mathbf{K}_A' = \mathbf{K}_A + \Delta \mathbf{K}_AKA′​=KA​+ΔKA​

• Updated Precision Score:

  PK′=0.6,MK′=0.4P_K' = 0.6, \quad M_K' = 0.4PK′​=0.6,MK′​=0.4

4.2 Example 2: Human-AI Financial Forecasting

Context:

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

4.2.1 Incomplete Input/Output

• Issue: AI-Forecast lacks real-time stock data provided by Ms. Johnson.

• Detection:

  CD=∣DH∩DA∣∣DH∪DA∣=0.7C_D = \frac{|\mathbf{D}_H \cap \mathbf{D}_A|}{|\mathbf{D}_H \cup \mathbf{D}_A|} = 0.7CD​=∣DH​∪DA​∣∣DH​∩DA​∣​=0.7GD=0.3G_D = 0.3GD​=0.3

• Remediation:

  Ms. Johnson integrates real-time stock Data into AI-Forecast.

  DA′=DA∪(DH−DA)\mathbf{D}_A' = \mathbf{D}_A \cup (\mathbf{D}_H - \mathbf{D}_A)DA′​=DA​∪(DH​−DA​)CD′=1.0C_D' = 1.0CD′​=1.0

4.2.2 Inconsistent Input/Output

• Issue: Conflicting Information on market trends.

• Detection:

  SI=0.3,II=0.7S_I = 0.3, \quad I_I = 0.7SI​=0.3,II​=0.7

• Remediation:

  Reconcile conflicting Information by verifying data sources.

  IA′=IB′=IH+IA2\mathbf{I}_A' = \mathbf{I}_B' = \frac{\mathbf{I}_H + \mathbf{I}_A}{2}IA′​=IB′​=2IH​+IA​​

4.2.3 Imprecise Input/Output

• Issue: Vague Knowledge about demand forecasts.

• Detection:

  HK=2.0 bits,Hmax=2.0 bitsH_K = 2.0 \text{ bits}, \quad H_{\text{max}} = 2.0 \text{ bits}HK​=2.0 bits,Hmax​=2.0 bitsPK=0.0,MK=1.0P_K = 0.0, \quad M_K = 1.0PK​=0.0,MK​=1.0

• Remediation:

  Provide specific numerical projections for demand forecasts.

  KA′=KA+ΔKA\mathbf{K}_A' = \mathbf{K}_A + \Delta \mathbf{K}_AKA′​=KA​+ΔKA​PK′=0.8,MK′=0.2P_K' = 0.8, \quad M_K' = 0.2PK′​=0.8,MK′​=0.2

4.3 Example 3: Human-AI Educational Tutoring

Context:

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

4.3.1 Incomplete Input/Output

• Issue: AI-Tutor lacks comprehensive Knowledge about Alex's learning style.

• Detection:

  CK=∣KA∩KX∣∣KA∪KX∣=0.5C_K = \frac{|\mathbf{K}_A \cap \mathbf{K}_X|}{|\mathbf{K}_A \cup \mathbf{K}_X|} = 0.5CK​=∣KA​∪KX​∣∣KA​∩KX​∣​=0.5GK=0.5G_K = 0.5GK​=0.5

• Remediation:

  Alex provides detailed information about learning preferences.

  KA′=KA∪(KX−KA)\mathbf{K}_A' = \mathbf{K}_A \cup (\mathbf{K}_X - \mathbf{K}_A)KA′​=KA​∪(KX​−KA​)CK′=1.0C_K' = 1.0CK′​=1.0

4.3.2 Inconsistent Input/Output

• Issue: Conflicting Information about learning progress.

• Detection:

  SI=0.4,II=0.6S_I = 0.4, \quad I_I = 0.6SI​=0.4,II​=0.6

• Remediation:

  Align Information through progress tracking updates.

  IA′=IX′=IA+IX2\mathbf{I}_A' = \mathbf{I}_X' = \frac{\mathbf{I}_A + \mathbf{I}_X}{2}IA′​=IX′​=2IA​+IX​​

4.3.3 Imprecise Input/Output

• Issue: Vague Knowledge explanations about calculus concepts.

• Detection:

  HK=1.8 bits,Hmax=2.0 bitsH_K = 1.8 \text{ bits}, \quad H_{\text{max}} = 2.0 \text{ bits}HK​=1.8 bits,Hmax​=2.0 bitsPK=0.1,MK=0.9P_K = 0.1, \quad M_K = 0.9PK​=0.1,MK​=0.9

• Remediation:

  AI-Tutor provides detailed semantic attributes and contextual examples.

  KA′=KA+ΔKA\mathbf{K}_A' = \mathbf{K}_A + \Delta \mathbf{K}_AKA′​=KA​+ΔKA​PK′=0.7,MK′=0.3P_K' = 0.7, \quad M_K' = 0.3PK′​=0.7,MK′​=0.3

5. Mathematical Optimization for 3-No Problems Conversion

To systematically address the 3-No Problems, we can frame the remediation as an optimization problem aimed at minimizing deficiencies while maximizing mutual understanding.

5.1 Objective Function

max⁡(UAB−λ⋅DAB)\max \left( \mathcal{U}_{AB} - \lambda \cdot \mathcal{D}_{AB} \right)max(UAB​−λ⋅DAB​)

Where:

• UAB\mathcal{U}_{AB}UAB​: Mutual Understanding measure between Stakeholder A and B.

• DAB\mathcal{D}_{AB}DAB​: Overall Deficiency measure, defined as:

  DAB=∑X∈{D,I,K,W,P}∥DefABX∥2\mathcal{D}_{AB} = \sum_{X \in \{D, I, K, W, P\}} \|\mathbf{Def}_{AB}^X\|_2DAB​=X∈{D,I,K,W,P}∑​∥DefABX​∥2​DefABX=[GXIXMX]\mathbf{Def}_{AB}^X = \begin{bmatrix} G_X \\ I_X \\ M_X \end{bmatrix}DefABX​=​GX​IX​MX​​​

• $\lambda$: Weighting factor balancing the importance of minimizing deficiencies against maximizing Understanding.

5.2 Constraints

Ensure that deficiencies do not exceed acceptable thresholds:

DAB≤θ\mathcal{D}_{AB} \leq \thetaDAB​≤θ

Where:

• $\theta$: Predefined threshold for maximum allowable deficiency.

5.3 Penalty Function

Incorporate penalties for exceeding thresholds:

Penalty=η⋅max⁡(0,DAB−θ)\text{Penalty} = \eta \cdot \max(0, \mathcal{D}_{AB} - \theta)Penalty=η⋅max(0,DAB​−θ)

Where:

• $\eta$: Penalty coefficient.

5.4 Combined Objective

Integrate the penalty into the objective function:

max⁡(UAB−λ⋅DAB−Penalty)\max \left( \mathcal{U}_{AB} - \lambda \cdot \mathcal{D}_{AB} - \text{Penalty} \right)max(UAB​−λ⋅DAB​−Penalty)

This formulation ensures that the optimization prioritizes enhancing Understanding while adhering to deficiency constraints.

6. Practical Implementation Steps6.1 Step 1: Data Collection and Profiling

• Action: Collect DIKWP profiles from both stakeholders.

• Tools: Data aggregation systems, profiling algorithms.

6.2 Step 2: Identification of 3-No Problems

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

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

6.3 Step 3: Quantification and Assessment

• Action: Calculate completeness scores, consistency scores, and precision scores.

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

6.4 Step 4: Remediation Strategy Formulation

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

• Tools: Decision support systems, optimization solvers.

6.5 Step 5: Implementation and Monitoring

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

• Tools: Feedback loops, iterative optimization processes.

7. Conclusion

The conversion of the 3-No Problems within the DIKWP*DIKWP interaction space is a structured process that involves identifying, quantifying, and remediating Incompleteness, Inconsistency, and Imprecision across the DIKWP components. By employing mathematical frameworks and targeted strategies, stakeholders can systematically address these communication deficiencies, thereby enhancing mutual understanding, reducing errors, and fostering effective collaboration. This comprehensive approach ensures that interactions are aligned with shared goals and cognitive frameworks, mitigating the risk of misunderstandings and improving overall interaction quality.

Future Directions:

• Advanced Detection Algorithms: Develop more sophisticated algorithms for real-time detection of 3-No Problems.

• Automated Remediation Systems: Create AI-driven systems that can autonomously address and rectify communication deficiencies.

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

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Acknowledgments

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.

Author Information

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

Keywords: DIKWP Model, 3-No Problems, Relativity of Hallucination, Human-AI Interaction, Cognitive Enclosure, Mathematical Framework, Data-Information-Knowledge-Wisdom-Purpose, Hallucination Mitigation, Understanding Enhancement