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

We will investigate into the 12 philoshophical problems by Prof. Yucong Duan using the DIKWP Semantic Mathematics framework proposed by Prof. Yucong Duan. This analysis will be more mathematical, incorporating the formal definitions, mathematical representations, and examples from the DIKWP Semantic Mathematics. We will systematically apply the mathematical formulations of Data (D), Information (I), Knowledge (K), Wisdom (W), and Purpose (P) to each philosophical problem, and explore the interactions between these components using the mathematical structures defined.

Overview:

The mind-body problem explores the relationship between mental states (mind) and physical brain states (body). It questions how subjective experiences arise from physical processes.

DIKWP Components:

• Data (D): Neural data, brain imaging results, physiological measurements.

• Information (I): Patterns and correlations identified between neural data and mental states.

• Knowledge (K): Theories explaining the mind-body relationship, such as dualism, physicalism.

• Wisdom (W): Ethical considerations regarding consciousness, personal identity, treatment of mental disorders.

• Purpose (P): Goals such as improving mental health treatments, understanding consciousness.

Mathematical Modeling:

1. Data Conceptualization

• Semantic Attribute Set (S):

  $S=\{\text{Neural activity patterns},\text{Brain regions involved}\}$

• Data Concept Set (D):

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

  Each data element $d$ represents a specific neural measurement sharing common attributes.

2. Information Conceptualization

• Information Semantics Processing Function (FI):

  $FI:D\to I$

  Transform neural data $D$ into information $I$ by identifying differences and patterns.

• Example:

• Identify correlations between neural patterns and subjective reports.

• $I=FI(D)$ includes mappings of neural data to information about neural correlates of consciousness.

3. Knowledge Conceptualization

• Knowledge Graph (K):

  $K=(N,E)$

• $N$: Concepts such as "consciousness," "neural correlates," "subjective experience."

• $E$: Relationships like "is associated with," "influences."

• Edges Representation:

  e=(ni,nj,r)e = (n_i, n_j, r)e=(ni​,nj​,r)

• For example, e1=(Neural Activity Pattern A,Subjective Experience B,"correlates with")e_1 = (\text{Neural Activity Pattern A}, \text{Subjective Experience B}, \text{"correlates with"})e1​=(Neural Activity Pattern A,Subjective Experience B,"correlates with")

• Knowledge Formation Function:

  $FK:I\to K$

• Abstracts information $I$ into structured knowledge $K$.

4. Wisdom Conceptualization

• Decision Function:

  W:{D,I,K,W,P}→D∗W: \{ D, I, K, W, P \} \rightarrow D^*W:{D,I,K,W,P}→D∗

• Processes all DIKWP components to generate optimal decisions D∗D^*D∗.

• Example:

• Integrate knowledge $K$ with ethical considerations to decide on appropriate treatments.

• Include wisdom regarding patient autonomy, consent, and well-being.

5. Purpose Conceptualization

• Purpose Tuple:

  $P=(\text{Input},\text{Output})$

• Input: Current understanding of mind-body interactions.

• Output: Desired goals, such as effective therapies, deeper understanding.

• Transformation Function:

  $T:\text{Input}\to \text{Output}$

• Plan research strategies to achieve the purpose.

Interactions and Transformations:

• Data to Information Transformation (D → I):

• Use $FI$ to map neural data to information about neural correlates.

• Mathematical Representation:

  $I=FI(D)$

• Information to Knowledge Transformation (I → K):

• Use $FK$ to form theories explaining mind-body relations.

  $K=FK(I)$

• Knowledge to Wisdom Transformation (K → W):

• Apply wisdom function to integrate knowledge with ethical considerations.

  W:K→D∗W: K \rightarrow D^*W:K→D∗

• Wisdom to Purpose Alignment (W → P):

• Align decisions with the overarching purpose $P$.

  $P=TWP(W)$

• Purpose to Data Influence (P → D):

• Purpose $P$ influences data collection strategies.

  D′=TPD(P)D' = TPD(P)D′=TPD(P)

Conclusion:

By mathematically modeling the mind-body problem using the DIKWP Semantic Mathematics, we see how data is transformed into information, structured into knowledge, applied wisely, and aligned with purpose. This formalism allows for precise analysis and highlights the interactions between components.

Overview:

The hard problem addresses why and how physical processes in the brain give rise to subjective experiences (qualia).

DIKWP Components:

• Data (D): Neural activity data, subjective experience reports.

• Information (I): Identification of the explanatory gap between physical processes and experiences.

• Knowledge (K): Theories attempting to explain consciousness.

• Wisdom (W): Acknowledgement of limitations, ethical considerations.

• Purpose (P): Develop a comprehensive theory of consciousness.

Mathematical Modeling:

1. Data Conceptualization

• Semantic Attribute Set (S):

  $S=\{\text{Neural measurements},\text{Subjective reports}\}$

• Data Concept Set (D):

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

2. Information Conceptualization

• Information Semantics Processing Function (FI):

  $FI:D\to I$

• Identify differences constituting the explanatory gap.

• Example:

• $I=FI(D)$ captures the lack of direct correlation between neural data and subjective experiences.

3. Knowledge Conceptualization

• Knowledge Graph (K):

  $K=(N,E)$

• $N$: Concepts like "physical processes," "subjective experience," "explanatory gap."

• $E$: Relationships such as "does not fully explain."

• Knowledge Formation Function:

  $FK:I\to K$

4. Wisdom Conceptualization

• Decision Function:

  W:{D,I,K,W,P}→D∗W: \{ D, I, K, W, P \} \rightarrow D^*W:{D,I,K,W,P}→D∗

• Decide on research directions while acknowledging limitations.

5. Purpose Conceptualization

• Purpose Tuple:

  $P=(\text{Input},\text{Output})$

• Input: Incomplete understanding.

• Output: New theoretical developments.

Interactions and Transformations:

• Data to Information (D → I):

  $I=FI(D)$

• Information to Knowledge (I → K):

  $K=FK(I)$

• Purpose to Knowledge Influence (P → K):

  K′=TPK(P)K' = TPK(P)K′=TPK(P)

Conclusion:

Mathematical modeling highlights the challenges in achieving completeness in knowledge ($K$) due to the explanatory gap. The formalism shows limitations in transforming information ($I$) into a complete and consistent knowledge system.

Overview:

Examines whether human actions are freely chosen or determined by prior states.

DIKWP Components:

• Data (D): Observations of decision-making processes, neurological data.

• Information (I): Patterns indicating deterministic or random behaviors.

• Knowledge (K): Theories on free will and determinism.

• Wisdom (W): Ethical implications for moral responsibility.

• Purpose (P): Understanding human agency, informing societal norms.

Mathematical Modeling:

1. Data Conceptualization

• Semantic Attribute Set (S):

  $S=\{\text{Behavioral data},\text{Neural responses}\}$

• Data Concept Set (D):

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

2. Information Conceptualization

• Information Semantics Processing Function (FI):

  $FI:D\to I$

• Identify differences suggesting free will or determinism.

• Example:

• $I=FI(D)$ includes information on patterns of decision-making.

3. Knowledge Conceptualization

• Knowledge Formation Function:

  $FK:I\to K$

• Formulate philosophical theories.

4. Wisdom Conceptualization

• Decision Function:

  W:{D,I,K,W,P}→D∗W: \{ D, I, K, W, P \} \rightarrow D^*W:{D,I,K,W,P}→D∗

• Apply ethical considerations to knowledge.

5. Purpose Conceptualization

• Purpose Tuple:

  $P=(\text{Input},\text{Output})$

• Input: Current theories and data.

• Output: Policies reflecting understanding.

Interactions and Transformations:

• Data to Information (D → I):

  $I=FI(D)$

• Information to Knowledge (I → K):

  $K=FK(I)$

• Knowledge to Wisdom (K → W):

  D∗=W(K)D^* = W(K)D∗=W(K)

• Purpose to Data Influence (P → D):

  D′=TPD(P)D' = TPD(P)D′=TPD(P)

Conclusion:

Mathematical modeling illustrates the transformation of data into knowledge and its application in ethical decision-making, aligned with societal purposes.

Overview:

Explores whether moral principles are universal or culturally dependent.

DIKWP Components:

• Data (D): Cultural practices, moral codes from various societies.

• Information (I): Differences and similarities in moral practices.

• Knowledge (K): Ethical theories, principles.

• Wisdom (W): Application of ethical knowledge considering diversity.

• Purpose (P): Promote understanding, respect diversity, enhance well-being.

Mathematical Modeling:

1. Data Conceptualization

• Semantic Attribute Set (S):

  $S=\{\text{Moral codes},\text{Cultural practices}\}$

• Data Concept Set (D):

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

2. Information Conceptualization

• FI: D → I

• Identify differences in moral codes.

3. Knowledge Conceptualization

• FK: I → K

• Formulate ethical theories.

4. Wisdom Conceptualization

• W: { D, I, K, W, P } \rightarrow D^ *

• Apply knowledge to promote understanding.

5. Purpose Conceptualization

• P = (\text{Input}, \text{Output})

• Input: Varied moral practices.

• Output: Ethical frameworks respecting diversity.

Interactions and Transformations:

• Similar to previous problems, with emphasis on ethical considerations.

Completeness:

• Knowledge (K): Should be logically complete, covering all relevant propositions derived from information ($I$).

• Mathematical Representation:

• $K=\{\varphi \mid \varphi \text{ is a logical consequence of }I\}$

• Completeness Criterion:

• For any proposition $\varphi$ in the language $L$, $\varphi \in K$ or $\neg \varphi \in K$.

Consistency:

• Knowledge (K): Must be free from contradictions.

• Consistency Criterion:

• $\nexists \varphi$ such that $\varphi \in K$ and $\neg \varphi \in K$.

Application to Problems:

• In each philosophical problem, we assess whether the knowledge formed satisfies logical completeness and consistency.

• Example for the Mind-Body Problem:

• Ensure that all propositions about the relationship between mind and body are accounted for.

• Check that no contradictions exist within the theoretical frameworks.

Interconnected Knowledge Graphs:

• Nodes: Concepts from different philosophical problems.

• Edges: Relationships between concepts.

• Mathematical Representation:

• Ntotal=⋃iNiN_{total} = \bigcup_{i} N_iNtotal​=⋃i​Ni​

• Etotal=⋃iEiE_{total} = \bigcup_{i} E_iEtotal​=⋃i​Ei​

• Unified Knowledge Graph Ktotal=(Ntotal,Etotal)K_{total} = (N_{total}, E_{total})Ktotal​=(Ntotal​,Etotal​)

• Implications:

• Shared concepts and theories enhance the completeness of the overall knowledge system.

• Cross-problem analysis can identify inconsistencies or reinforce consistency.

By applying the DIKWP Semantic Mathematics to the philosophical problems, we have provided a mathematical analysis of the transformations and interactions between Data (D), Information (I), Knowledge (K), Wisdom (W), and Purpose (P). This approach allows for a precise, structured understanding of complex cognitive processes and highlights the mathematical underpinnings of philosophical inquiries.

Note to the Reader

This analysis has aimed to provide a mathematical perspective on the application of the DIKWP model to philosophical problems, incorporating the detailed definitions and mathematical formulations provided. If you desire further mathematical detail on specific problems or aspects, please let me know, and I will expand on those areas.

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. ".

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