Examples of the 3-No Problems in 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, effective communication between stakeholders—whether human or artificial intelligence (AI) systems—is crucial for achieving mutual understanding and collaboration. However, this communication is often hindered by three primary issues collectively termed the 3-No Problems: Incomplete Input/Output, Inconsistent Input/Output, and Imprecise Input/Output. This document provides detailed, concrete examples illustrating these problems within the DIKWP*DIKWP interaction space, focusing on the semantics of Data ("sameness"), Information ("difference"), and Knowledge ("completeness"). These examples demonstrate how the 3-No Problems manifest in real-world scenarios and highlight strategies for their identification and remediation based on the provided DIKWP standards.

1. Introduction

The DIKWP model structures cognitive processes into five interconnected components: Data, Information, Knowledge, Wisdom, and Purpose. Communication between stakeholders involves the exchange of these components, but deficiencies can disrupt this process. The 3-No Problems—Incomplete, Inconsistent, and Imprecise Input/Output—are critical barriers to effective communication and understanding. This document elucidates these problems through detailed examples aligned with the DIKWP model's standardized semantics, emphasizing mathematical representations within the DIKWP*DIKWP interaction space.

2. Overview of DIKWP Semantic Components

Before delving into the 3-No Problems, it is essential to understand the standardized semantics of the DIKWP components as defined in the provided standard:

• Data (D): Represents "sameness" through shared semantic attributes S={f1,f2,…,fn}S = \{f_1, f_2, \dots, f_n\}S={f1​,f2​,…,fn​}. Data concepts are collections of semantic instances sharing the same or probabilistically approximate semantic attributes.

• Information (I): Represents "difference" through varying semantic attributes D={g1,g2,…,gm}D = \{g_1, g_2, \dots, g_m\}D={g1​,g2​,…,gm​}. Information semantics highlight distinctions and relationships between Data concepts.

• Knowledge (K): Represents "completeness" through comprehensive semantic attributes C={h1,h2,…,hk}C = \{h_1, h_2, \dots, h_k\}C={h1​,h2​,…,hk​}. Knowledge semantics encapsulate a full understanding of concepts, integrating Data and Information into a coherent framework.

• Wisdom (W): Involves ethical and contextual judgments based on Knowledge.

• Purpose (P): The driving goals or intentions guiding cognitive processes.

Each stakeholder’s DIKWP profile is mathematically represented as:

Profilei={Di,Ii,Ki,Wi,Pi}\text{Profile}_i = \{\mathbf{D}_i, \mathbf{I}_i, \mathbf{K}_i, \mathbf{W}_i, \mathbf{P}_i\}Profilei​={Di​,Ii​,Ki​,Wi​,Pi​}

Where:

• Di∈Rn\mathbf{D}_i \in \mathbb{R}^nDi​∈Rn: Data vector

• Ii∈Rm\mathbf{I}_i \in \mathbb{R}^mIi​∈Rm: Information vector

• Ki∈Rp\mathbf{K}_i \in \mathbb{R}^pKi​∈Rp: Knowledge vector

• Wi∈Rq\mathbf{W}_i \in \mathbb{R}^qWi​∈Rq: Wisdom vector

• Pi∈Rr\mathbf{P}_i \in \mathbb{R}^rPi​∈Rr: Purpose vector

The semantic space enables the quantification of similarities and differences between these vectors, facilitating the analysis of communication effectiveness and the identification of the 3-No Problems.

3. Mathematical Semantics of the 3-No Problems3.1 Incomplete Input/Output (No-Incomplete)

Definition:

Incomplete Input/Output occurs when one stakeholder lacks sufficient Data ("sameness") to fully comprehend the DIKWP components being communicated by the other stakeholder. This deficiency in shared semantic attributes $S$ leads to gaps in understanding.

Data Conceptualization:

In the DIKWP model, Data semantics represent specific manifestations of the same semantics in cognition. Each Data concept $d\in D$ shares a common set of semantic attributes $S$, enabling cognitive entities to categorize different instances under the same concept based on shared semantics.

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. Therefore, the collection of Data concepts is defined as:

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

Mathematical Representation:

Given two stakeholders, Sender (A) and Receiver (B), for the Data component $D$:

• Data Sets:

DA={dA1,dA2,…,dAn}\mathbf{D}_A = \{ d_{A1}, d_{A2}, \dots, d_{An} \}DA​={dA1​,dA2​,…,dAn​}DB={dB1,dB2,…,dBm}\mathbf{D}_B = \{ d_{B1}, d_{B2}, \dots, d_{Bm} \}DB​={dB1​,dB2​,…,dBm​}

Each $d\in D$ shares the semantic attributes $S$, ensuring "sameness."

• Completeness Score CDC_DCD​:

CD=∣DA∩DB∣∣DA∪DB∣C_D = \frac{|\mathbf{D}_A \cap \mathbf{D}_B|}{|\mathbf{D}_A \cup \mathbf{D}_B|}CD​=∣DA​∪DB​∣∣DA​∩DB​∣​

Where:

• 0≤CD≤10 \leq C_D \leq 10≤CD​≤1

• CD=1C_D = 1CD​=1 indicates complete overlap (no incompleteness)

• CD<1C_D < 1CD​<1 indicates incompleteness

Gap Identification:

GD=1−CD=∣DA∪DB∣−∣DA∩DB∣∣DA∪DB∣G_D = 1 - C_D = \frac{|\mathbf{D}_A \cup \mathbf{D}_B| - |\mathbf{D}_A \cap \mathbf{D}_B|}{|\mathbf{D}_A \cup \mathbf{D}_B|}GD​=1−CD​=∣DA​∪DB​∣∣DA​∪DB​∣−∣DA​∩DB​∣​

Impact on Understanding:

Incomplete Data leads to gaps in understanding, hindering the formation of a coherent Knowledge base and potentially resulting in misunderstandings or erroneous conclusions.

Remediation Mechanism:

To address incompleteness, the sender provides the missing Data components:

ΔDA=DA−DB\Delta \mathbf{D}_A = \mathbf{D}_A - \mathbf{D}_BΔDA​=DA​−DB​DB′=DB∪ΔDA\mathbf{D}_B' = \mathbf{D}_B \cup \Delta \mathbf{D}_ADB′​=DB​∪ΔDA​

Where:

• ΔDA\Delta \mathbf{D}_AΔDA​ represents the missing Data elements from Sender A.

• DB′\mathbf{D}_B'DB′​ is the updated Receiver B’s Data component after integration.

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. The effectiveness of their collaboration depends on the exchange and integration of Data, Information, and Knowledge within the DIKWP framework.

Detailed Example:

1. Data Exchange:

• Extensive medical datasets including millions of patient records

• Research articles on respiratory diseases

• Patient's age: 45

• Symptoms: Persistent cough, fever, shortness of breath

• Medical history: No prior respiratory issues

• Dr. Smith's Data (DH\mathbf{D}_HDH​):

• AI-Diagnosis's Data (DA\mathbf{D}_ADA​):

2. Identifying Incompleteness:

• Duration: Comprehensive datasets cover varying durations

• Intensity: Detailed records with intensity scales

• Duration: 2 weeks

• Intensity: Moderate

• Shared Semantic Attributes $S$: The Data concepts "patient symptoms" should share attributes like duration, intensity, and associated factors.

• Dr. Smith's Data Subset for Symptoms:

• AI-Diagnosis's Data Subset for Symptoms:

• Completeness Score CDC_DCD​:

  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

  Here, Dr. Smith provides specific patient data, but AI-Diagnosis has a broader dataset. The overlap is partial, indicating incompleteness.

3. Impact on Understanding:

• Gap Identification GDG_DGD​:

  GD=1−CD=1−0.6=0.4G_D = 1 - C_D = 1 - 0.6 = 0.4GD​=1−CD​=1−0.6=0.4

• The AI lacks specific patient data nuances that Dr. Smith possesses, leading to a gap in the Data component.

4. Remediation Mechanism:

• Dr. Smith provides additional Data to AI-Diagnosis:

  DA′=DA∪ΔDH\mathbf{D}_A' = \mathbf{D}_A \cup \Delta \mathbf{D}_HDA′​=DA​∪ΔDH​

• Integration of Missing Data:

  ΔDH=DH−DA={Patient’s age: 45,Medical history: No prior respiratory issues}\Delta \mathbf{D}_H = \mathbf{D}_H - \mathbf{D}_A = \{\text{Patient's age: 45}, \text{Medical history: No prior respiratory issues}\}ΔDH​=DH​−DA​={Patient’s age: 45,Medical history: No prior respiratory issues}

• Updated Completeness Score CD′C_D'CD′​:

  CD′=∣DH∩DA′∣∣DH∪DA′∣=55=1.0C_D' = \frac{|\mathbf{D}_H \cap \mathbf{D}_A'|}{|\mathbf{D}_H \cup \mathbf{D}_A'|} = \frac{5}{5} = 1.0CD′​=∣DH​∪DA′​∣∣DH​∩DA′​∣​=55​=1.0

• Result: The Completeness Gap is eliminated (GD′=0G_D' = 0GD′​=0), enabling AI-Diagnosis to utilize all relevant Data for accurate analysis.

5. Conclusion:

   By addressing the incompleteness in the Data component through the integration of missing semantic attributes, Dr. Smith and AI-Diagnosis enhance their mutual understanding, leading to a more accurate and reliable diagnosis.

3.2 Inconsistent Input/Output (No-Inconsistent)

Definition:

Inconsistent Input/Output arises when there are conflicting Information ("difference") between the DIKWP components of the two stakeholders, leading to confusion and misunderstanding. This inconsistency stems from differing semantic attributes $D$ associated with Information concepts.

Information Conceptualization:

In the DIKWP model, Information semantics represent "difference" by highlighting varying semantic attributes and associations. Each Information concept $i\in I$ may possess unique or differing semantic attributes $D$, reflecting distinctions and variations in the data.

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:

Given two stakeholders, Sender (A) and Receiver (B), for the Information component $I$:

• Information Sets:

IA={iA1,iA2,…,iAn}\mathbf{I}_A = \{ i_{A1}, i_{A2}, \dots, i_{An} \}IA​={iA1​,iA2​,…,iAn​}IB={iB1,iB2,…,iBm}\mathbf{I}_B = \{ i_{B1}, i_{B2}, \dots, i_{Bm} \}IB​={iB1​,iB2​,…,iBm​}

Each $i\in I$ may possess unique semantic attributes, ensuring "difference."

• Consistency Score SIS_ISI​:

Using cosine similarity:

SI=IA⋅IB∥IA∥∥IB∥S_I = \frac{\mathbf{I}_A \cdot \mathbf{I}_B}{\|\mathbf{I}_A\| \|\mathbf{I}_B\|}SI​=∥IA​∥∥IB​∥IA​⋅IB​​

Where:

• 0≤SI≤10 \leq S_I \leq 10≤SI​≤1

• SI=1S_I = 1SI​=1 indicates perfect consistency

• SI<1S_I < 1SI​<1 indicates inconsistency

Inconsistency Quantification:

II=1−SII_I = 1 - S_III​=1−SI​

Impact on Understanding:

Inconsistencies disrupt the formation of a coherent Knowledge base, leading to confusion and potentially incorrect Wisdom application, undermining the Purpose of the interaction.

Conflict Resolution Mechanism:

To resolve inconsistencies, stakeholders engage in dialogue to reconcile conflicting Information components. A simple mathematical approach involves averaging the conflicting vectors:

IA′=IB′=IA+IB2\mathbf{I}_A' = \mathbf{I}_B' = \frac{\mathbf{I}_A + \mathbf{I}_B}{2}IA′​=IB′​=2IA​+IB​​

Alternatively, more sophisticated reconciliation algorithms can be employed based on context and stakeholder priorities.

Example Scenario: Human-AI Collaborative Financial Forecasting

Context:

A financial analyst (Ms. Johnson) collaborates with an AI forecasting system (AI-Forecast) to predict stock market trends. Their interaction involves exchanging Information derived from Data and Knowledge.

Detailed Example:

1. Information Exchange:

• Recent market trend: Bearish

• Key indicators: Rising interest rates, geopolitical tensions

• Recent market trend: Bullish

• Key indicators: Increasing GDP, low unemployment

• Ms. Johnson's Information (IH\mathbf{I}_HIH​):

• AI-Forecast's Information (IA\mathbf{I}_AIA​):

2. Identifying Inconsistency:

• Financial indicators: Interest rates, geopolitical factors

• Economic indicators: GDP growth, unemployment rates

• Semantic Attributes $D$: Indicators used to define market trends.

• Ms. Johnson's Information Semantic Attributes:

• AI-Forecast's Information Semantic Attributes:

• Consistency Score SIS_ISI​:

  SI=IH⋅IA∥IH∥∥IA∥=0.3S_I = \frac{\mathbf{I}_H \cdot \mathbf{I}_A}{\|\mathbf{I}_H\| \|\mathbf{I}_A\|} = 0.3SI​=∥IH​∥∥IA​∥IH​⋅IA​​=0.3

  A low similarity score indicates significant inconsistency.

3. Impact on Understanding:

• Inconsistency Measure III_III​:

  II=1−SI=1−0.3=0.7I_I = 1 - S_I = 1 - 0.3 = 0.7II​=1−SI​=1−0.3=0.7

• The conflicting Information leads to confusion about the actual market trend, impeding coherent Knowledge formation.

4. Conflict Resolution Mechanism:

• Resulting Information:

• Recent market trend: Neutral (Bullish and Bearish)

• Key indicators: Combination of GDP growth, unemployment rates, interest rates, and geopolitical factors

• Reconciliation through Averaging:

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

• Alternative Resolution: Engage in dialogue to prioritize certain indicators over others based on contextual relevance.

5. Conclusion:

   By reconciling inconsistent Information through averaging or dialogue, Ms. Johnson and AI-Forecast align their understanding, reducing confusion and facilitating the formation of a coherent Knowledge base for accurate financial forecasting.

3.3 Imprecise Input/Output (No-Imprecise)

Definition:

Imprecise Input/Output occurs when the Knowledge ("completeness") exchanged is vague or ambiguous, leading to misunderstandings in the DIKWP components. This imprecision arises from incomplete semantic attributes $C$ within Knowledge concepts.

Knowledge Conceptualization:

In the DIKWP model, Knowledge semantics represent "completeness" by encapsulating comprehensive semantic attributes that provide a full understanding of concepts. Each Knowledge concept $k\in K$ aims to cover all necessary semantic attributes $C$ for completeness.

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.

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

Mathematical Representation:

Given two stakeholders, Sender (A) and Receiver (B), for the Knowledge component $K$:

• Knowledge Sets:

KA={kA1,kA2,…,kAn}\mathbf{K}_A = \{ k_{A1}, k_{A2}, \dots, k_{An} \}KA​={kA1​,kA2​,…,kAn​}KB={kB1,kB2,…,kBm}\mathbf{K}_B = \{ k_{B1}, k_{B2}, \dots, k_{Bm} \}KB​={kB1​,kB2​,…,kBm​}

Each $k\in K$ should ideally cover all necessary semantic attributes for "completeness."

• Entropy-Based Precision Score PKP_KPK​:

PK=1−HKHmaxP_K = 1 - \frac{H_K}{H_{\text{max}}}PK​=1−Hmax​HK​​

Where:

• HKH_KHK​ is the Shannon entropy of the Knowledge component $K$, measuring uncertainty or ambiguity.

• HmaxH_{\text{max}}Hmax​ is the maximum possible entropy for component $K$.

Entropy HKH_KHK​ is calculated as:

HK=−∑i=1Np(ki)log⁡p(ki)H_K = -\sum_{i=1}^{N} p(k_i) \log p(k_i)HK​=−i=1∑N​p(ki​)logp(ki​)

Where:

• p(ki)p(k_i)p(ki​) is the probability of occurrence of the ithi^{th}ith element in $K$.

Imprecision Quantification:

MK=1−PK=HKHmaxM_K = 1 - P_K = \frac{H_K}{H_{\text{max}}}MK​=1−PK​=Hmax​HK​​

Impact on Understanding:

Imprecise Knowledge introduces ambiguity, making it challenging to accurately interpret and integrate Knowledge, thereby impeding the formation of coherent Wisdom and alignment with Purpose.

Clarification Mechanism:

To mitigate imprecision, stakeholders seek clarification:

Clarified Component KA′=KA+ΔKA\text{Clarified Component } \mathbf{K}_A' = \mathbf{K}_A + \Delta \mathbf{K}_AClarified Component KA′​=KA​+ΔKA​Clarified Component KB′=KB+ΔKB\text{Clarified Component } \mathbf{K}_B' = \mathbf{K}_B + \Delta \mathbf{K}_BClarified Component KB′​=KB​+ΔKB​

Where:

• ΔKA\Delta \mathbf{K}_AΔKA​ and ΔKB\Delta \mathbf{K}_BΔKB​ represent the clarified and disambiguated additions to the respective Knowledge components.

Example Scenario: Human-AI Collaborative Educational Tutoring

Context:

A student (Alex) interacts with an AI tutoring system (AI-Tutor) to learn calculus. The effectiveness of the learning process depends on the precise exchange and integration of Knowledge.

Detailed Example:

1. Knowledge Exchange:

• Calculus Concept: Derivative

• Explanation: "The derivative represents the slope of the tangent line to the function at a given point."

• Calculus Concept: Derivative

• Explanation: "The derivative measures how a function changes as its input changes."

• AI-Tutor's Knowledge (KA\mathbf{K}_AKA​):

• Alex's Knowledge (KX\mathbf{K}_XKX​):

2. Identifying Imprecision:

• Definition: Specific geometric interpretation (slope of tangent)

• Applications: Not explicitly mentioned

• Definition: Basic explanation

• Applications: Limited (e.g., basic change measurement)

• Semantic Attributes $C$: Comprehensive understanding of the derivative concept, including definitions, applications, and properties.

• AI-Tutor's Knowledge Attributes:

• Alex's Knowledge Attributes:

• Entropy-Based Precision Score PKP_KPK​:

  HK=−(12log⁡12+12log⁡12)=1 bitH_K = -\left( \frac{1}{2} \log \frac{1}{2} + \frac{1}{2} \log \frac{1}{2} \right) = 1 \text{ bit}HK​=−(21​log21​+21​log21​)=1 bitHmax=log⁡2(N)=2 bits(assuming N=4)H_{\text{max}} = \log_2(N) = 2 \text{ bits} \quad (\text{assuming } N = 4)Hmax​=log2​(N)=2 bits(assuming N=4)PK=1−12=0.5P_K = 1 - \frac{1}{2} = 0.5PK​=1−21​=0.5

• Imprecision Measure MKM_KMK​:

  MK=1−PK=0.5M_K = 1 - P_K = 0.5MK​=1−PK​=0.5

  A moderate imprecision measure indicates significant ambiguity in the Knowledge exchange.

3. Impact on Understanding:

• Ambiguity in Definitions: The AI-Tutor's explanation lacks the geometric interpretation that Alex is familiar with, leading to potential misunderstandings.

• Incomplete Semantic Coverage: The AI-Tutor does not fully cover the applications of derivatives, limiting Alex's comprehensive understanding.

4. Clarification Mechanism:

• Clarified Knowledge Addition (ΔKA\Delta \mathbf{K}_AΔKA​):

• Geometric Interpretation: "The derivative at a point is the slope of the tangent line to the function at that point."

• Applications: "Derivatives are used to find local maxima and minima, optimize functions, and model real-world phenomena involving rates of change."

• AI-Tutor Enhances Knowledge:

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

• Updated Precision Scores:

  HK′=−(34log⁡34+14log⁡14)≈0.81 bitsH_K' = -\left( \frac{3}{4} \log \frac{3}{4} + \frac{1}{4} \log \frac{1}{4} \right) \approx 0.81 \text{ bits}HK′​=−(43​log43​+41​log41​)≈0.81 bitsPK′=1−0.812=0.595P_K' = 1 - \frac{0.81}{2} = 0.595PK′​=1−20.81​=0.595MK′=0.405M_K' = 0.405MK′​=0.405

  The imprecision measure decreases, indicating enhanced clarity and completeness in Knowledge.

5. Conclusion:

   By addressing imprecision through the addition of detailed semantic attributes, the AI-Tutor provides a more comprehensive and precise understanding of calculus concepts. This refinement facilitates Alex's learning process, ensuring that Knowledge exchange is clear, complete, and unambiguous.

4. Integrating the 3-No Problems into the DIKWP*DIKWP Framework4.1 Comprehensive Interaction Model

The interaction between two stakeholders, considering the 3-No Problems, is modeled as:

Interaction=EntityA×EntityB={DAB,IAB,KAB,WAB,PAB}\text{Interaction} = \text{Entity}_A \times \text{Entity}_B = \{\mathbf{D}_{AB}, \mathbf{I}_{AB}, \mathbf{K}_{AB}, \mathbf{W}_{AB}, \mathbf{P}_{AB}\}Interaction=EntityA​×EntityB​={DAB​,IAB​,KAB​,WAB​,PAB​}

Where each component XAB\mathbf{X}_{AB}XAB​ is adjusted based on the presence of Incompleteness, Inconsistency, and Imprecision:

XAB′=fX(XA,XB)−Remediation Terms\mathbf{X}_{AB}' = f_X(\mathbf{X}_A, \mathbf{X}_B) - \text{Remediation Terms}XAB′​=fX​(XA​,XB​)−Remediation Terms

Remediation terms are functions that address GXG_XGX​, IXI_XIX​, and MXM_XMX​ for each $X\in \{D,I,K,W,P\}$.

4.2 Unified Mathematical Representation

To encapsulate all three No Problems, define a Deficiency Vector DefABX\mathbf{Def}_{AB}^XDefABX​ for each component $X$:

DefABX=[GXIXMX]\mathbf{Def}_{AB}^X = \begin{bmatrix} G_X \\ I_X \\ M_X \end{bmatrix}DefABX​=​GX​IX​MX​​​

Where:

• GXG_XGX​: Completeness Gap (from Incompleteness)

• IXI_XIX​: Inconsistency Measure (from Inconsistency)

• MXM_XMX​: Imprecision Measure (from Imprecision)

Define the Overall Deficiency Measure DAB\mathcal{D}_{AB}DAB​ as the aggregation of deficiencies across all DIKWP components:

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​

Where ∥⋅∥2\|\cdot\|_2∥⋅∥2​ denotes the Euclidean norm, providing a scalar value representing the total deficiency in the interaction.

4.3 Optimization for Enhanced Understanding

The objective is to minimize DAB\mathcal{D}_{AB}DAB​ while maximizing mutual Understanding UAB\mathcal{U}_{AB}UAB​:

max⁡UAB−λ⋅DAB\max \quad \mathcal{U}_{AB} - \lambda \cdot \mathcal{D}_{AB}maxUAB​−λ⋅DAB​

Where $\lambda$ is a weighting factor balancing the importance of minimizing deficiencies against maximizing Understanding.

5. Remediation Strategies for the 3-No Problems

The remediation strategies for each of the 3-No Problems involve enhancing the respective DIKWP components to bridge gaps, resolve inconsistencies, and clarify imprecisions.

5.1 Remedied Connectivities (Addressing Incompleteness)

• Objective: Ensure that all relevant semantic attributes $S$ in Data are shared between stakeholders to achieve full "sameness."

• Mechanism:

1. Identify Missing Data: Determine which semantic attributes $S$ are absent.

2. Provide Missing Data: Share the missing Data components to fill the gaps.

• Outcome: Complete semantic overlap (CD=1C_D = 1CD​=1) eliminates gaps in understanding.

Example Application:

In the Human-AI Medical Diagnosis scenario, Dr. Smith identifies that the AI-Diagnosis lacks specific patient Data (age and medical history). By providing this missing Data, the Completeness Gap GDG_DGD​ is eliminated, ensuring that the AI has all necessary information to accurately analyze the patient's condition.

5.2 Eliminating Inconsistencies

• Objective: Align conflicting Information semantics $D$ to achieve coherence.

• Mechanism:

1. Quantify Inconsistency: Measure the similarity SIS_ISI​ and calculate III_III​.

2. Reconcile Conflicts: Use averaging or dialogue to align the Information components.

• Outcome: Reduced inconsistency (III_III​ decreases), leading to coherent Knowledge integration.

Example Application:

In the Human-AI Financial Forecasting scenario, Ms. Johnson and AI-Forecast initially have conflicting Information about market trends. By reconciling this inconsistency through averaging or dialogue, they align their understanding, reducing confusion and facilitating a coherent Knowledge base for accurate financial forecasting.

5.3 Reducing Imprecision

• Objective: Enhance the completeness of Knowledge semantics $C$ to eliminate ambiguity.

• Mechanism:

1. Assess Precision: Calculate the Precision Score PKP_KPK​ and Imprecision Measure MKM_KMK​.

2. Clarify Knowledge: Add detailed semantic attributes $C$ to reduce entropy HKH_KHK​.

• Outcome: Lower imprecision (MKM_KMK​ decreases), ensuring clear and comprehensive Knowledge understanding.

Example Application:

In the Human-AI Educational Tutoring scenario, Alex receives imprecise Knowledge about calculus derivatives from AI-Tutor. By enhancing the Knowledge with detailed semantic attributes (geometric interpretation and applications), the imprecision measure MKM_KMK​ decreases, ensuring that Alex gains a clear and comprehensive understanding of the concept.

6. Conclusion

The 3-No Problems—Incomplete, Inconsistent, and Imprecise Input/Output—are fundamental challenges within the DIKWP*DIKWP interaction framework that impede effective communication and mutual understanding between stakeholders. Through detailed examples aligned with the standardized semantics of Data ("sameness"), Information ("difference"), and Knowledge ("completeness"), this document has illustrated how these problems manifest in real-world scenarios and the strategies for their remediation. Addressing these deficiencies enhances the reliability and coherence of interactions, mitigates the risk of hallucinations in AI systems, and fosters more effective human-AI collaboration, ensuring that interactions are aligned with shared goals and cognitive frameworks.

Future research should focus on refining these mathematical models, integrating advanced optimization techniques, and conducting empirical studies to validate the framework in diverse real-world scenarios. Such advancements will significantly contribute to the fields of cognitive science and artificial intelligence, promoting more reliable and harmonious human-AI interactions.

References

1. Duan, Y. (2024). International Test and Evaluation Standards for Artificial Intelligence based on Networked Data-Information-Knowledge-Wisdom-Purpose (DIKWP) Model.

2. Vaswani, A., et al. (2017). Attention is all you need. Advances in Neural Information Processing Systems, 5998–6008.

3. Sutton, R. S., & Barto, A. G. (2018). Reinforcement Learning: An Introduction. MIT Press.

4. Bengio, Y., LeCun, Y., & Hinton, G. (2015). Deep learning. Nature, 521(7553), 436–444.

5. Silver, D., et al. (2016). Mastering the game of Go with deep neural networks and tree search. Nature, 529(7587), 484–489.

6. Marcus, G., & Davis, E. (2020). GPT-3, Bloviator: OpenAI's language generator has no idea what it's talking about. MIT Technology Review.

7. Maynez, J., Narayan, S., Bohnet, B., & McDonald, R. (2020). On faithfulness and factuality in abstractive summarization. Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, 1906–1919.

8. Kant, I. (1781). Critique of Pure Reason.

9. Seth, A. K. (2014). A predictive processing theory of sensorimotor contingencies: Explaining the puzzle of perceptual presence and its absence in synesthesia. Cognitive Neuroscience, 5(2), 97–118.

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