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 between stakeholders, whether human or artificial intelligence (AI) systems, is fundamental to achieving mutual understanding and collaboration. Within the Data-Information-Knowledge-Wisdom-Purpose (DIKWP) model, communication processes can be impeded by three primary issues collectively termed the 3-No Problems: Incomplete Input/Output, Inconsistent Input/Output, and Imprecise Input/Output. This document provides a detailed mathematical exposition of these problems within the DIKWP model's standardized semantic space, focusing on the semantics of Data ("sameness"), Information ("difference"), and Knowledge ("completeness"). By formally defining, quantifying, and analyzing these issues based on the provided DIKWP standards, we aim to facilitate their identification and remediation, thereby enhancing the reliability and effectiveness of DIKWP*DIKWP interactions between stakeholders.

Communication between stakeholders involves the exchange of cognitive components encapsulated within the DIKWP framework. However, this process is often impeded by deficiencies that disrupt the seamless transformation and integration of Data, Information, Knowledge, Wisdom, and Purpose. These deficiencies, known as the 3-No Problems, are:

1. Incomplete Input/Output (No-Incomplete)

2. Inconsistent Input/Output (No-Inconsistent)

3. Imprecise Input/Output (No-Imprecise)

Understanding these problems within the standardized semantic space of the DIKWP model is crucial for enhancing mutual understanding and reducing the occurrence of hallucinations—erroneous perceptions or outputs—especially in human-AI collaborations.

The DIKWP model categorizes cognitive processes into five interconnected components:

1. Data (D): Raw, unprocessed facts or observations, representing "sameness" through shared semantic attributes.

2. Information (I): Processed data highlighting patterns and relationships, representing "difference" through varying semantic attributes.

3. Knowledge (K): Organized and contextualized information forming a coherent understanding, representing "completeness" through comprehensive semantic attributes.

4. Wisdom (W): Judgments and decisions based on Knowledge, incorporating ethical and contextual considerations.

5. 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.

Definition:

Incomplete Input/Output occurs when one stakeholder lacks sufficient Data ("sameness") to fully comprehend the DIKWP components being communicated by the other stakeholder.

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:

In a medical diagnosis scenario, if the AI (Sender A) lacks specific patient Data that the human (Receiver B) possesses, the human must provide this missing Data to the AI to enhance the Completeness Score for the Data component.

Definition:

Inconsistent Input/Output arises when there are conflicting Information ("difference") between the DIKWP components of the two stakeholders, leading to confusion and misunderstanding.

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:

If the AI suggests a diagnosis that conflicts with the human’s medical expertise, averaging the Information vectors or engaging in further dialogue can reconcile the inconsistency.

Definition:

Imprecise Input/Output occurs when the Knowledge ("completeness") exchanged is vague or ambiguous, leading to misunderstandings in the DIKWP components.

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:

In an educational AI tutor, if the AI provides vague feedback, specifying precise Knowledge and contextual examples can reduce imprecision, enhancing the student’s Understanding.

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 $X\in \{D,I,K,W,P\}$.

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.

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.

Objective: Maximize the Completeness Score CXC_XCX​ to ensure robust connectivity across DIKWP components.

Mechanism:

1. Identify Missing Components:

ΔXA=XA−XB\Delta \mathbf{X}_A = \mathbf{X}_A - \mathbf{X}_BΔXA​=XA​−XB​

1. Integrate Missing Data/Information:

XB′=XB∪ΔXA\mathbf{X}_B' = \mathbf{X}_B \cup \Delta \mathbf{X}_AXB′​=XB​∪ΔXA​

Example:

In a medical diagnosis scenario, if the AI lacks specific patient Data that the human possesses, the human must provide this missing Data to the AI to enhance the Completeness Score for the Data component.

Objective: Minimize the Inconsistency Measure IXI_XIX​ to ensure alignment and coherence in DIKWP components.

Mechanism:

1. Calculate Consistency Scores SXS_XSX​:

SX=sim(XA,XB)=XA⋅XB∥XA∥∥XB∥S_X = \text{sim}(\mathbf{X}_A, \mathbf{X}_B) = \frac{\mathbf{X}_A \cdot \mathbf{X}_B}{\|\mathbf{X}_A\| \|\mathbf{X}_B\|}SX​=sim(XA​,XB​)=∥XA​∥∥XB​∥XA​⋅XB​​

1. Identify and Quantify Inconsistencies IX=1−SXI_X = 1 - S_XIX​=1−SX​:

2. Resolve Conflicts through Reconciliation:

A simple approach involves averaging the conflicting vectors:

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

Alternatively, implement more sophisticated reconciliation algorithms based on context and stakeholder priorities.

Example:

If the AI suggests a diagnosis that conflicts with the human’s medical expertise, averaging the Information vectors or engaging in further dialogue can reconcile the inconsistency.

Objective: Minimize the Imprecision Measure MXM_XMX​ to ensure clarity and precision in DIKWP components.

Mechanism:

1. Calculate Precision Scores PX=1−MXP_X = 1 - M_XPX​=1−MX​:

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

1. Identify Imprecise Components:

2. Clarify and Disambiguate Content:

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​

Where ΔXA\Delta \mathbf{X}_AΔXA​ and ΔXB\Delta \mathbf{X}_BΔXB​ represent the clarified and disambiguated additions to the respective Knowledge components.

Example:

In an educational AI tutor, if the AI provides vague feedback, specifying precise Knowledge and contextual examples can reduce imprecision, enhancing the student’s Understanding.

Formulate an optimization problem to maximize Understanding while minimizing Deficiency:

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

Where:

• UAB\mathcal{U}_{AB}UAB​: Mutual Understanding measure

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

• $\lambda$: Weighting factor balancing the trade-off

Ensure that deficiencies do not exceed acceptable thresholds:

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

Where:

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

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

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.

A medical practitioner (Human) collaborates with an AI diagnostic system (AI) to diagnose a patient's condition. Their interaction involves sharing and integrating DIKWP components to achieve an accurate diagnosis.

• Human (ProfileH\text{Profile}_HProfileH​):

• Data (DH\mathbf{D}_HDH​): Patient symptoms, medical history.

• Information (IH\mathbf{I}_HIH​): Identified potential diagnoses.

• Knowledge (KH\mathbf{K}_HKH​): Medical expertise and clinical guidelines.

• Wisdom (WH\mathbf{W}_HWH​): Ethical considerations in patient care.

• Purpose (PH\mathbf{P}_HPH​): Accurate and timely diagnosis.

• AI (ProfileA\text{Profile}_AProfileA​):

• Data (DA\mathbf{D}_ADA​): Extensive medical datasets, research articles.

• Information (IA\mathbf{I}_AIA​): Pattern recognition in patient data.

• Knowledge (KA\mathbf{K}_AKA​): Compiled medical knowledge from training data.

• Wisdom (WA\mathbf{W}_AWA​): Predefined ethical guidelines.

• Purpose (PA\mathbf{P}_APA​): Assist in diagnosis and treatment planning.

1. Data Exchange:

• Human to AI: Sends patient Data (DH\mathbf{D}_HDH​) to AI.

• Gap Identification: AI identifies any missing Data components relevant for diagnosis.

2. Information Sharing:

• AI Analysis: Processes DH\mathbf{D}_HDH​ to generate Information (IA\mathbf{I}_AIA​).

• Shared Information: AI communicates patterns and potential diagnoses back to the Human.

3. Knowledge Integration:

• Human Review: Evaluates AI's Information (IA\mathbf{I}_AIA​) against personal Knowledge (KH\mathbf{K}_HKH​).

• Knowledge Update: Human incorporates relevant Knowledge from AI into KH\mathbf{K}_HKH​.

4. Wisdom Application:

• Ethical Judgment: Both stakeholders apply Wisdom (WH\mathbf{W}_HWH​ and WA\mathbf{W}_AWA​) to ensure ethical considerations in diagnosis.

5. Purpose Alignment:

• Goal Confirmation: Both entities confirm their Purpose (PH\mathbf{P}_HPH​ and PA\mathbf{P}_APA​) to ensure alignment towards accurate diagnosis.

• Mathematical Optimization: Adjust DIKWP components to minimize DHA\mathcal{D}_{HA}DHA​ and maximize UHA\mathcal{U}_{HA}UHA​.

max⁡UHA−λ⋅DHA\max \quad \mathcal{U}_{HA} - \lambda \cdot \mathcal{D}_{HA}maxUHA​−λ⋅DHA​

• Result: Enhanced Understanding leads to a more accurate and reliable diagnosis, reducing the likelihood of AI-generated hallucinations (erroneous diagnoses).

The 3-No Problems—Incomplete, Inconsistent, and Imprecise Input/Output—are critical challenges within the DIKWP*DIKWP interaction framework that impede effective communication and mutual Understanding between stakeholders. By establishing precise mathematical semantics for these problems based on standardized DIKWP components—Data semantics corresponding to "sameness," Information semantics corresponding to "difference," and Knowledge semantics corresponding to "completeness"—stakeholders can systematically identify and remediate deficiencies. This structured approach 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.

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