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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 ComponentsSpace | 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 |
Mapping/Function | Mathematical Representation | From Space | To Space | Role |
---|---|---|---|---|
Semantic Assignment (ϕ\phiϕ) | ϕ:C→S\phi: C \rightarrow Sϕ:C→S | ConC (Concepts) | SemA (Semantics) | Assigns meanings to concepts |
Extraction Function (ψ\psiψ) | ψ:S→C\psi: S \rightarrow Cψ:S→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 (ggg) | 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 (Φ\PhiΦ) | 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 (Θ\ThetaΘ) | 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 (κ\kappaκ) | 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 |
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 |
From Space | To Space | Mapping/Function | DIKWP Concepts Involved | DIKWP Semantics Involved |
---|---|---|---|---|
ConC | SemA | Semantic Assignment (ϕ\phiϕ) | Concepts CCC | Meanings SSS assigned to concepts |
SemA | ConC | Extraction Function (ψ\psiψ) | Concepts CCC extracted from semantics | Semantics SSS providing context for concept extraction |
SemA | ConN | Cognitive Function (fif_ifi) | Cognitive functions fif_ifi processing semantics | Meanings SSS being transformed into information III or knowledge KKK |
ConN | SemA | Generation Function (ggg) | Information III, Knowledge KKK producing new semantics | New semantics S′S'S′ generated from cognitive processing |
ConN | Conscious Space | Consciousness Function (Φ\PhiΦ) | Cognitive functions FConNF_{\text{ConN}}FConN | Emergent wisdom WWW integrating ethical considerations |
Conscious Space | ConN | Modulation Function (Θ\ThetaΘ) | Adjusted cognitive functions FConN′F_{\text{ConN}}'FConN′ | Wisdom WWW influencing cognitive processing |
ConN | ConC | Abstraction Function (κ\kappaκ) | 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 |
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 |
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 |
Function | Application in Example | Result |
---|---|---|
ϕ\phiϕ | 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 |
Φ\PhiΦ | 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 |
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 |
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
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
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. ".
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