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, hinges on the seamless interaction of their cognitive frameworks. Prof. Yucong Duan's Data-Information-Knowledge-Wisdom-Purpose (DIKWP) model provides a structured approach to understanding these cognitive processes. However, communication is often impeded by the 3-No Problems: Incomplete, Inconsistent, and Imprecise Input/Output. This paper presents a mathematical framework to formally define and quantify these problems within the DIKWP*DIKWP interaction model. By establishing precise mathematical semantics, we aim to facilitate the identification, measurement, and remediation of these deficiencies, thereby enhancing mutual Understanding and reducing the incidence of hallucinations in human-AI collaborations.

In the DIKWP*DIKWP interaction framework, two stakeholders interact by exchanging Data, Information, Knowledge, Wisdom, and Purpose. However, this communication process is often marred by three primary issues collectively termed the 3-No Problems:

1. Incomplete Input/Output: Missing data or information leading to gaps in understanding.

2. Inconsistent Input/Output: Conflicting data or information causing confusion.

3. Imprecise Input/Output: Vague or ambiguous data leading to misunderstandings.

To systematically address these challenges, it is essential to develop a mathematical semantics that can precisely define, measure, and remediate these problems within the DIKWP*DIKWP framework.

Each stakeholder's DIKWP profile is represented as a set of vectors in a high-dimensional semantic space:

Entityi={Di,Ii,Ki,Wi,Pi}\text{Entity}_i = \{\mathbf{D}_i, \mathbf{I}_i, \mathbf{K}_i, \mathbf{W}_i, \mathbf{P}_i\}Entityi​={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 interaction between two entities, Entity A and Entity B, 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​}

Each component of the interaction is a function of the corresponding components of the individual entities:

XAB=fX(XA,XB)∀X∈{D,I,K,W,P}\mathbf{X}_{AB} = f_X(\mathbf{X}_A, \mathbf{X}_B) \quad \forall X \in \{D, I, K, W, P\}XAB​=fX​(XA​,XB​)∀X∈{D,I,K,W,P}

Where fXf_XfX​ defines the transformation rules for each DIKWP component during interaction.

Definition: Incomplete Input/Output occurs when one stakeholder lacks sufficient data or information to fully comprehend the DIKWP components being communicated by the other stakeholder.

For each DIKWP component $X$, define the Completeness Score CXC_XCX​ as the ratio of the intersecting elements to the union of elements between the sender and receiver:

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:

• 0≤CX≤10 \leq C_X \leq 10≤CX​≤1

• CX=1C_X = 1CX​=1 implies complete overlap (no incompleteness)

• CX<1C_X < 1CX​<1 indicates incompleteness

The Completeness Gap GXG_XGX​ quantifies the extent of incompleteness:

GX=1−CX=∣XA∪XB∣−∣XA∩XB∣∣XA∪XB∣G_X = 1 - C_X = \frac{|\mathbf{X}_A \cup \mathbf{X}_B| - |\mathbf{X}_A \cap \mathbf{X}_B|}{|\mathbf{X}_A \cup \mathbf{X}_B|}GX​=1−CX​=∣XA​∪XB​∣∣XA​∪XB​∣−∣XA​∩XB​∣​

To remediate incompleteness, the sender must provide the missing components:

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

The receiver updates their profile:

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

Definition: Inconsistent Input/Output arises when there are conflicting data or information between the DIKWP components of the two stakeholders, leading to confusion and misunderstanding.

For each DIKWP component $X$, define the Consistency Score SXS_XSX​ using a similarity measure (e.g., cosine similarity):

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​​

Where:

• 0≤SX≤10 \leq S_X \leq 10≤SX​≤1

• SX=1S_X = 1SX​=1 implies perfect consistency

• SX<1S_X < 1SX​<1 indicates inconsistency

The Inconsistency Measure IXI_XIX​ quantifies the level of inconsistency:

IX=1−SXI_X = 1 - S_XIX​=1−SX​

To resolve inconsistencies, stakeholders engage in dialogue to reconcile conflicting components:

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​​

This averaging approach assumes both stakeholders agree to a middle ground. Alternatively, more sophisticated reconciliation algorithms can be employed based on context and priorities.

Definition: Imprecise Input/Output occurs when the data or information exchanged is vague or ambiguous, leading to misunderstandings in the DIKWP components.

For each DIKWP component $X$, define the Precision Score PXP_XPX​ as the inverse of the entropy HXH_XHX​:

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

Where:

• HXH_XHX​ is the entropy of component $X$, measuring uncertainty or ambiguity.

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

Entropy HXH_XHX​ can be calculated using Shannon's entropy formula if $X$ is discrete:

HX=−∑i=1Np(xi)log⁡p(xi)H_X = -\sum_{i=1}^{N} p(x_i) \log p(x_i)HX​=−i=1∑N​p(xi​)logp(xi​)

Where p(xi)p(x_i)p(xi​) is the probability of occurrence of the ithi^{th}ith element in $X$.

The Imprecision Measure MXM_XMX​ quantifies the level of imprecision:

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

To mitigate imprecision, stakeholders seek clarification:

Clarified Component XA′=XA+ΔXA\text{Clarified Component } \mathbf{X}_A' = \mathbf{X}_A + \Delta \mathbf{X}_AClarified Component XA′​=XA​+ΔXA​Clarified Component XB′=XB+ΔXB\text{Clarified Component } \mathbf{X}_B' = \mathbf{X}_B + \Delta \mathbf{X}_BClarified Component XB′​=XB​+ΔXB​

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

The interaction between two entities, considering the 3-No Problems, can be modeled as follows:

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 DefAB\mathbf{Def}_{AB}DefAB​ 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

• IXI_XIX​: Inconsistency Measure

• MXM_XMX​: Imprecision Measure

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.

To enhance connectivity and address incompleteness:

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

Where ΔXA=XA−XB\Delta \mathbf{X}_A = \mathbf{X}_A - \mathbf{X}_BΔXA​=XA​−XB​ ensures that the receiver incorporates all missing elements from the sender.

To eliminate inconsistencies:

XA′=XA∩XB\mathbf{X}_A' = \mathbf{X}_A \cap \mathbf{X}_BXA′​=XA​∩XB​XB′=XA∩XB\mathbf{X}_B' = \mathbf{X}_A \cap \mathbf{X}_BXB′​=XA​∩XB​

This intersection ensures that both stakeholders retain only the consistent elements of their DIKWP components.

To reduce imprecision:

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 DIKWP components, enhancing precision.

Maximize Understanding while minimizing Deficiency:

max⁡XABUAB−λ⋅DAB\max_{\mathbf{X}_{AB}} \quad \mathcal{U}_{AB} - \lambda \cdot \mathcal{D}_{AB}XAB​max​UAB​−λ⋅DAB​

Ensure that each deficiency measure stays within acceptable thresholds:

GX≤θG∀XG_X \leq \theta_G \quad \forall XGX​≤θG​∀XIX≤θI∀XI_X \leq \theta_I \quad \forall XIX​≤θI​∀XMX≤θM∀XM_X \leq \theta_M \quad \forall XMX​≤θM​∀X

Where θG\theta_GθG​, θI\theta_IθI​, and θM\theta_MθM​ are predefined thresholds for completeness, consistency, and precision respectively.

Incorporate penalties for exceeding thresholds:

Penalty=∑XηG⋅max⁡(0,GX−θG)+ηI⋅max⁡(0,IX−θI)+ηM⋅max⁡(0,MX−θM)\text{Penalty} = \sum_{X} \eta_G \cdot \max(0, G_X - \theta_G) + \eta_I \cdot \max(0, I_X - \theta_I) + \eta_M \cdot \max(0, M_X - \theta_M)Penalty=X∑​ηG​⋅max(0,GX​−θG​)+ηI​⋅max(0,IX​−θI​)+ηM​⋅max(0,MX​−θM​)

Where ηG\eta_GηG​, ηI\eta_IηI​, and ηM\eta_MηM​ are penalty coefficients.

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

This ensures that both Understanding is maximized and Deficiencies are minimized, with penalties enforcing adherence to thresholds.

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 GapX\text{Gap}_XGapX​ and maximize UHA\mathcal{U}_{HA}UHA​.

• 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 in the DIKWP*DIKWP interaction framework that impede effective communication and mutual Understanding between stakeholders. By formalizing the mathematical semantics of these problems, we enable precise identification, quantification, and remediation within the interaction process. This structured approach not only enhances mutual Understanding but also mitigates the risk of hallucinations in both human and AI systems, fostering more reliable and coherent collaborations.

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