Tables of Conceptual Space, Semantic Space, Cognitive Space, and Conscious 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)

Introduction

To enhance understanding and provide clarity, we will present detailed tables that summarize the modeling of the mutual expressing capabilities among the Conceptual Space (ConC), Semantic Space (SemA), Cognitive Space (ConN), and Conscious Space, using the DIKWP (Data, Information, Knowledge, Wisdom, Purpose) mathematical model. We will explicitly distinguish between DIKWP concepts and DIKWP semantics in each table.

Table 1: Overview of Spaces and DIKWP Components

Space	DIKWP Focus	DIKWP Concepts	DIKWP Semantics
Conceptual Space (ConC)	Data (D), Knowledge (K)	Definitions, structures of data and knowledge (e.g., concepts, nodes, relationships)	Symbolic representations without inherent meanings
Semantic Space (SemA)	Information (I)	Meanings derived from data concepts	Contextual interpretations and associations of concepts
Cognitive Space (ConN)	Transformations among D, I, K, W	Cognitive functions and processes (e.g., transformations, operations)	Dynamic interpretation and manipulation of meanings
Conscious Space	Wisdom (W), Purpose (P)	Emergent understanding, ethical reasoning, goal alignment	Subjective experiences and ethical considerations guiding actions

Table 2: Mapping Functions and Their Roles

Mapping/Function	Mathematical Representation	From Space	To Space	Role
Semantic Assignment ($\varphi$)	$\varphi :C\to S$	ConC (Concepts)	SemA (Semantics)	Assigns meanings to concepts
Extraction Function ($\psi$)	$\psi :S\to C$	SemA (Semantics)	ConC (Concepts)	Extracts concepts from semantics
Cognitive Function (fif_ifi​)	fi:S→If_i: S \rightarrow Ifi​:S→I or fi:S→Kf_i: S \rightarrow Kfi​:S→K	SemA (Semantics)	ConN (Concepts/Semantics)	Processes meanings to generate information or knowledge
Generation Function ($g$)	g:I or K→S′g: I \text{ or } K \rightarrow S'g:I or K→S′	ConN (Concepts/Semantics)	SemA (Semantics)	Generates new semantics from cognitive processing
Consciousness Function ($\Phi$)	Φ:FConN→W\Phi: F_{\text{ConN}} \rightarrow WΦ:FConN​→W	ConN (Cognitive Functions)	Conscious Space (Wisdom)	Emergence of wisdom and conscious understanding
Modulation Function ($\Theta$)	Θ:W→FConN′\Theta: W \rightarrow F_{\text{ConN}}'Θ:W→FConN′​	Conscious Space (Wisdom)	ConN (Cognitive Functions)	Adjusts cognitive functions based on conscious insights
Abstraction Function ($\kappa$)	κ:FConN→C′\kappa: F_{\text{ConN}} \rightarrow C'κ:FConN​→C′	ConN (Cognitive Functions)	ConC (Concepts)	Abstracts cognitive processes into new concepts
Purpose Alignment Function (TW→PT_{\text{W→P}}TW→P​)	TW→P:W→PT_{\text{W→P}}: W \rightarrow PTW→P​:W→P	Conscious Space (Wisdom)	Purpose (P)	Aligns wisdom with goals and objectives

Table 3: Distinction Between DIKWP Concepts and Semantics in Each Space

Space	DIKWP Concepts	DIKWP Semantics
Conceptual Space (ConC)	- Definitions of data and knowledge elements- Structural relationships (nodes and edges)	- Symbols without inherent meanings- Abstract representations
Semantic Space (SemA)	- Meanings assigned to concepts- Contextual information	- Interpretations and associations- Dynamic meanings derived from context
Cognitive Space (ConN)	- Cognitive functions and processes- Transformation operations	- Dynamic manipulation of meanings- Interpretations leading to new understanding
Conscious Space	- Emergent wisdom and ethical reasoning- Alignment with purpose	- Subjective experiences- Ethical considerations guiding decisions

Table 4: Mutual Expressing Capabilities Among Spaces

From Space	To Space	Mapping/Function	DIKWP Concepts Involved	DIKWP Semantics Involved
ConC	SemA	Semantic Assignment ($\varphi$)	Concepts $C$	Meanings $S$ assigned to concepts
SemA	ConC	Extraction Function ($\psi$)	Concepts $C$ extracted from semantics	Semantics $S$ providing context for concept extraction
SemA	ConN	Cognitive Function (fif_ifi​)	Cognitive functions fif_ifi​ processing semantics	Meanings $S$ being transformed into information $I$ or knowledge $K$
ConN	SemA	Generation Function ($g$)	Information $I$, Knowledge $K$ producing new semantics	New semantics S′S'S′ generated from cognitive processing
ConN	Conscious Space	Consciousness Function ($\Phi$)	Cognitive functions FConNF_{\text{ConN}}FConN​	Emergent wisdom $W$ integrating ethical considerations
Conscious Space	ConN	Modulation Function ($\Theta$)	Adjusted cognitive functions FConN′F_{\text{ConN}}'FConN′​	Wisdom $W$ influencing cognitive processing
ConN	ConC	Abstraction Function ($\kappa$)	New concepts C′C'C′ derived from cognitive processes	Abstracted meanings contributing to concept formation
Conscious Space	Purpose (P)	Purpose Alignment (TW→PT_{\text{W→P}}TW→P​)	Action plans aligned with wisdom	Ethical and purposeful semantics guiding actions

Table 5: Limitations and Challenges in Mutual Expressions

Interaction	Limitations	Impact on DIKWP Concepts	Impact on DIKWP Semantics
ConC ↔ SemA	- Ambiguity in mapping concepts to semantics- Information loss in inverse mapping	- Potential confusion in concept definitions	- Loss of semantic nuances- Reduced clarity in meanings
SemA ↔ ConN	- Complex transformations- Representational differences	- Cognitive functions may not capture all concept details	- Semantics may change unpredictably- Difficulty in interpretation
ConN ↔ Conscious Space	- Subjectivity of conscious experiences- Non-linear influence on cognition	- Cognitive processes may not fully explain consciousness	- Ethical considerations may be hard to formalize
ConN ↔ ConC	- Abstraction may omit procedural details- Static concepts may not capture dynamics	- New concepts may lack depth- Incomplete representation of processes	- Semantics may not reflect dynamic changes- Potential oversimplification

Table 6: Example of AI-Powered Decision Support SystemA. Concepts and Semantics in Each Space

Space	DIKWP Concepts	DIKWP Semantics
ConC	- "Market Data", "Ethical Guidelines", "Risk Assessment"- Nodes and relationships in knowledge graphs	- Definitions without context- Structural representations
SemA	- Meanings of market trends- Ethical implications in contexts	- Interpretation of market data- Cultural considerations
ConN	- Cognitive functions like fAnalysisf_{\text{Analysis}}fAnalysis​, fDecisionf_{\text{Decision}}fDecision​	- Processing of meanings to generate insights- Dynamic reasoning
Conscious Space	- Emergent wisdom wRecommendationw_{\text{Recommendation}}wRecommendation​- Ethical decision-making	- Ethical significance of recommendations- Alignment with long-term goals

B. Mapping Functions Applied

Function	Application in Example	Result
$\varphi$	ϕ("Market Data")=sMarket Data\phi(\text{"Market Data"}) = s_{\text{Market Data}}ϕ("Market Data")=sMarket Data​	Assigns meaning to "Market Data" concept
fAnalysisf_{\text{Analysis}}fAnalysis​	fAnalysis(sMarket Trends)=iInsightsf_{\text{Analysis}}(s_{\text{Market Trends}}) = i_{\text{Insights}}fAnalysis​(sMarket Trends​)=iInsights​	Processes market trends semantics to generate insights
$\Phi$	wRecommendation=Φ(fDecision)w_{\text{Recommendation}} = \Phi(f_{\text{Decision}})wRecommendation​=Φ(fDecision​)	Emergence of wisdom from decision function
TW→PT_{\text{W→P}}TW→P​	pAction Plan=TW→P(wRecommendation)p_{\text{Action Plan}} = T_{\text{W→P}}(w_{\text{Recommendation}})pAction Plan​=TW→P​(wRecommendation​)	Aligns wisdom with purpose to create an action plan

C. Distinctions in the Example

Aspect	DIKWP Concept	DIKWP Semantics
"Market Data"	Defined term representing collected data	Meaning indicating consumer behavior trends
Cognitive Function fAnalysisf_{\text{Analysis}}fAnalysis​	Process that analyzes semantics to produce insights	Interpretation of market trends leading to actionable information
Wisdom wRecommendationw_{\text{Recommendation}}wRecommendation​	Emergent understanding guiding decisions	Ethical implications and long-term impact of recommendations
Action Plan pAction Planp_{\text{Action Plan}}pAction Plan​	Structured plan derived from wisdom and purpose	Intended outcomes aligned with goals and ethical considerations

Table 7: Key Takeaways

Observation	Explanation
Clear Distinction Enhances Modeling	Differentiating between concepts and semantics improves clarity
Mappings Connect Spaces Through DIKWP Components	Functions and mappings transform concepts and semantics across spaces
Limitations Highlight Modeling Challenges	Recognizing limitations aids in refining models and approaches
DIKWP Framework Integrates Cognitive Processes	Provides a structured approach to model complex interactions
Ethical Considerations are Central in Conscious Space	Wisdom and purpose guide actions with ethical implications

Conclusion

By presenting detailed tables, we have clarified the mutual expressing capabilities among the spaces using the DIKWP mathematical model, explicitly distinguishing between DIKWP concepts and DIKWP semantics. The tables highlight:

• The roles and interactions of each space within the DIKWP framework.

• The mathematical functions and mappings that enable transformations between concepts and semantics.

• The limitations and challenges inherent in modeling these complex interactions.

• An example that illustrates how these concepts and semantics manifest in a practical application.

Understanding these distinctions and relationships is crucial for:

• Developing AI systems that effectively integrate data, information, knowledge, wisdom, and purpose.

• Modeling cognitive processes with precision and clarity.

• Addressing ethical considerations in decision-making processes.

References for Further Study

• Duan, Y. (Year). Relevant publications on DIKWP Semantic Mathematics and cognitive modeling.

• Cognitive Science Literature: Exploring the role of concepts and semantics in cognition.

• Artificial Intelligence Texts: For understanding cognitive functions and AI system design.

• Ethics in AI: Guidelines and discussions on integrating ethical considerations in AI systems.

Note: The mathematical representations and functions provided are conceptual and serve to illustrate the relationships among the spaces within the DIKWP framework. Actual implementations may require more detailed and context-specific mathematical formulations.

References for Further Reading

1. International Standardization Committee of Networked DIKWP for Artificial Intelligence Evaluation (DIKWP-SC),World Association of Artificial Consciousness(WAC),World Conference on Artificial Consciousness(WCAC). Standardization of DIKWP Semantic Mathematics of International Test and Evaluation Standards for Artificial Intelligence based on Networked Data-Information-Knowledge-Wisdom-Purpose (DIKWP ) Model. October 2024 DOI: 10.13140/RG.2.2.26233.89445 .  https://www.researchgate.net/publication/384637381_Standardization_of_DIKWP_Semantic_Mathematics_of_International_Test_and_Evaluation_Standards_for_Artificial_Intelligence_based_on_Networked_Data-Information-Knowledge-Wisdom-Purpose_DIKWP_Model

2. Duan, Y. (2023). The Paradox of Mathematics in AI Semantics. Proposed by Prof. Yucong Duan:" As Prof. Yucong Duan proposed the Paradox of Mathematics as that current mathematics will not reach the goal of supporting real AI development since it goes with the routine of based on abstraction of real semantics but want to reach the reality of semantics. ".

转载本文请联系原作者获取授权，同时请注明本文来自段玉聪科学网博客。
链接地址：https://blog.sciencenet.cn/blog-3429562-1458205.html

上一篇：Toward Artificial Consciousness with ConC, SemA, ConN（初学者版）
下一篇：Expressing Capabilities Among 4 Spaces with DIKWP Math（初学者版）