DIKWP Operations on 

Conscious, Cognitive, Semantic, Conceptual Spaces

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)

We propose comprehensive explanation of the renewed operations on the DIKWP model based on the modified framework and the integration of the four spaces—Conceptual Space (ConC), Cognitive Space (ConN), Semantic Space (SemA), and Conscious Space—and their interactions and transformations. This expanded explanation will delve deeply into each aspect, incorporating the foundational principles, formal definitions, examples, and implications, as per your request.

Artificial intelligence (AI) aims to create machines capable of performing tasks that typically require human intelligence, such as understanding natural language, reasoning, learning, and problem-solving. Traditional mathematics has provided formal foundations for AI development. However, Prof. Yucong Duan identifies a fundamental paradox in traditional mathematics concerning AI semantics:

Paradox of Mathematics in AI Semantics: Traditional mathematics abstracts away real-world semantics to create generalizable models, yet AI requires these very semantics to achieve genuine understanding. This detachment hinders AI from truly comprehending and interacting with the world as humans do.

To resolve this paradox, Prof. Duan proposes a modified Data-Information-Knowledge-Wisdom-Purpose (DIKWP) Semantic Mathematics framework, emphasizing the intrinsic integration of semantics into mathematical constructs, mirroring human cognitive development.

The objective is to renew the operations on the DIKWP model by integrating it with the four spaces—Conceptual Space (ConC), Cognitive Space (ConN), Semantic Space (SemA), and Conscious Space—to address the paradox and enhance AI's capability to process and represent semantics meaningfully.

The modified DIKWP framework is built upon three fundamental semantics, reflecting basic human cognitive processes:

1. Sameness (Data): Recognition of shared attributes or identities between entities.

2. Difference (Information): Identification of distinctions or disparities between entities.

3. Completeness (Knowledge): Integration of all relevant attributes and relationships to form holistic concepts.

These fundamental semantics serve as the building blocks for higher-level cognitive constructs, such as Wisdom and Purpose.

• Definition: The space where concepts are defined, organized, and related.

• Role: Houses definitions and structures of concepts derived from Data (Sameness) and Knowledge (Completeness).

• Function: Organizes DIKWP components by categorizing and mapping them through conceptual relationships.

• Definition: The dynamic processing environment where DIKWP components are transformed into understanding and actions through cognitive functions.

• Role: Processes Information (Difference) by transforming inputs into understanding.

• Function: Executes cognitive operations such as perception, attention, memory, reasoning, and decision-making.

• Definition: The network of semantic associations between concepts.

• Role: Maintains the meanings and relationships of concepts, reflecting the fundamental semantics of Data, Information, and Knowledge.

• Function: Ensures semantic consistency and integrity across cognitive processes.

• Definition: The layer where consciousness emerges from the interactions of cognition and semantics.

• Role: Represents awareness and higher-order cognitive processes, including the application of Wisdom and Purpose.

• Function: Integrates operations of ConN and SemA with self-awareness, enabling metacognition and self-regulation.

By integrating the four spaces, we can renew the operations on the DIKWP model to enhance its semantic processing capabilities.

• Data is recognized through the fundamental semantic of Sameness within the Conceptual Space (ConC).

• Objective: To identify and aggregate entities sharing common attributes.

• Aggregation (AGG): Combines entities sharing common attributes to form composite concepts.

  Mathematical Representation:

  AGG(e1,e2,...,en)=ecomposite\text{AGG}(e_1, e_2, ..., e_n) = e_{\text{composite}}AGG(e1​,e2​,...,en​)=ecomposite​

• e1,e2,...,ene_1, e_2, ..., e_ne1​,e2​,...,en​: Entities with shared attributes.

• ecompositee_{\text{composite}}ecomposite​: Composite entity representing the aggregated concept.

• Entities: Individual sheep (e1,e2,...,ene_1, e_2, ..., e_ne1​,e2​,...,en​) with attributes like "woolly coat," "four legs."

• Operation: Aggregate these entities in ConC to form the concept of "sheep" (esheepe_{\text{sheep}}esheep​).

• Process:

• AGG(e1,e2,...,en)=esheep\text{AGG}(e_1, e_2, ..., e_n) = e_{\text{sheep}}AGG(e1​,e2​,...,en​)=esheep​

• $A=\{\text{woolly coat},\text{four legs}\}$

1. Identify Shared Attributes (SemA):

2. Aggregate Entities (ConC):

• Semantic Space (SemA): Provides the shared semantic attributes that justify the aggregation.

• Cognitive Space (ConN): Processes sensory inputs to recognize sameness.

• Conscious Space: May reflect on the concept formation if awareness is involved.

• Information arises from the fundamental semantic of Difference processed within the Cognitive Space (ConN).

• Objective: To identify distinctions between entities and generate new semantic associations.

• Differentiation (DIFF): Identifies differences between entities or attributes.

  Mathematical Representation:

  DIFF(ei,ej)={a∣a∈A,a distinguishes ei from ej}\text{DIFF}(e_i, e_j) = \{ a \mid a \in A, a \text{ distinguishes } e_i \text{ from } e_j \}DIFF(ei​,ej​)={a∣a∈A,a distinguishes ei​ from ej​}

• ei,eje_i, e_jei​,ej​: Entities being compared.

• $A$: Set of attributes.

• $a$: Attribute that distinguishes eie_iei​ from eje_jej​.

• Information Processing Function (FIF_IFI​):

  FI:X→YF_I: X \rightarrow YFI​:X→Y

• $X$: Input semantics (e.g., Data, existing Knowledge).

• $Y$: Output semantics (new Information).

• Scenario: Noticing that one sheep (eie_iei​) is black while others (eje_jej​) are white.

• Process:

• Incorporate "color" as a variable attribute in the concept of "sheep."

• FI:Sheep Data→Sheep Color Variation InformationF_I: \text{Sheep Data} \rightarrow \text{Sheep Color Variation Information}FI​:Sheep Data→Sheep Color Variation Information

• $a=\text{color}$

• DIFF(ei,ej)={black vs. white}\text{DIFF}(e_i, e_j) = \{ \text{black vs. white} \}DIFF(ei​,ej​)={black vs. white}

1. Identify Distinguishing Attribute (SemA):

2. Generate New Information (ConN):

3. Update Conceptual Space (ConC):

• Semantic Space (SemA): Provides attributes used to identify differences.

• Conceptual Space (ConC): Updates concepts based on new information.

• Cognitive Space (ConN): Executes differentiation to generate information.

• Conscious Space: May become aware of the new information, leading to further reflection.

• Knowledge represents Completeness, integrating attributes and relations to form holistic concepts.

• Objective: To form structured understanding and abstract generalizations.

• Integration (INT): Combines attributes and relations to form complete concepts.

  Mathematical Representation:

  INT(ei)={ak,rij∣ak∈A,rij∈R}\text{INT}(e_i) = \{ a_k, r_{ij} \mid a_k \in A, r_{ij} \in R \}INT(ei​)={ak​,rij​∣ak​∈A,rij​∈R}

• eie_iei​: Entity.

• aka_kak​: Attributes of eie_iei​.

• rijr_{ij}rij​: Relations between eie_iei​ and other entities eje_jej​.

• Abstraction (ABST): Forms abstract concepts by integrating multiple entities.

  Mathematical Representation:

  ABST(e1,e2,...,en)=eabstract\text{ABST}(e_1, e_2, ..., e_n) = e_{\text{abstract}}ABST(e1​,e2​,...,en​)=eabstract​

• Knowledge Representation:

• $N$: Set of concept nodes.

• $E$: Set of edges representing relationships.

• Semantic Networks:

  Mathematical Representation:

  $$K=(N,E)$$

• Scenario: Forming the knowledge that "All swans are white."

• Process:

• Create a semantic network where all swans are connected to the attribute "white."

• ABST(e1,e2,...,en)=eAll Swans are White\text{ABST}(e_1, e_2, ..., e_n) = e_{\text{All Swans are White}}ABST(e1​,e2​,...,en​)=eAll Swans are White​

• Attributes: acolor=whitea_{\text{color}} = \text{white}acolor​=white

• Relations: ris a(ei,Swan)r_{\text{is a}}(e_i, \text{Swan})ris a​(ei​,Swan)

1. Observation (ConN): Observe multiple swans (e1,e2,...,ene_1, e_2, ..., e_ne1​,e2​,...,en​) that are white.

2. Integration (ConC and SemA):

3. Abstraction (ConC):

4. Knowledge Formation:

• Semantic Space (SemA): Stores meanings and relationships.

• Cognitive Space (ConN): Processes and integrates information to form knowledge.

• Conceptual Space (ConC): Structures knowledge into organized frameworks.

• Conscious Space: May reflect on the validity of the knowledge, especially if contradictory evidence arises.

• Wisdom involves integrating ethics, morals, and values into decision-making.

• Objective: To guide actions considering broader implications and ethical considerations.

• Contextualization (CS): Incorporates context into semantic interpretations.

  Mathematical Representation:

  $$\text{CS}(e,C)=s$$

• $e$: Entity.

• $C$: Context.

• $s$: Semantic content in context.

• Temporal Semantic Function (TS): Accounts for changes in meaning over time.

  $$\text{TS}(e,t)=s$$

• $t$: Time.

• Intentional Semantic Function (IS): Reflects purpose or intention behind entities and actions.

  $$\text{IS}(e,I)=s$$

• $I$: Intention or purpose.

• Wisdom Decision Function:

  Mathematical Representation:

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

• $D$: Data.

• $I$: Information.

• $K$: Knowledge.

• $W$: Existing Wisdom.

• $P$: Purpose.

• D∗D^*D∗: Optimal decision.

• Scenario: Deciding whether to share a friend's confidential information.

• Process:

1. Data: Knowledge of the confidential information ($D$).

2. Information: Understanding the implications of sharing ($I$).

3. Knowledge: Recognizing trust and privacy principles ($K$).

4. Wisdom: Ethical considerations against breaching confidentiality ($W$).

5. Purpose: Desire to maintain trust and integrity ($P$).

6. Decision: Choose not to share the information (D∗D^*D∗).

• Conscious Space: Applies awareness and ethical considerations.

• Cognitive Space (ConN): Processes inputs considering Wisdom.

• Semantic Space (SemA): Embeds moral values into semantic associations.

• Conceptual Space (ConC): May update concepts of trust and confidentiality.

• Purpose provides goal-oriented direction, influencing transformations across all spaces.

• Objective: To guide cognitive activities towards desired outcomes.

• Transformation Function (T):

  Mathematical Representation:

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

• Transforms input semantics into output semantics based on Purpose.

• Intentionality Integration (IS):

  $$\text{IS}(e,I)=s$$

• Incorporates Purpose into semantic processing.

• Scenario: An AI assistant aims to optimize a user's daily schedule.

• Process:

• Constraints: Meeting times, deadlines.

• Preferences: User's peak productivity hours.

• $T:\text{Input}\to \text{Optimized Schedule}$

1. Input: User's appointments and tasks ($\text{Input}$).

2. Purpose: Maximize productivity and well-being ($P$).

3. Transformation (ConN):

4. Considerations:

5. Output: Adjusted schedule aligning with Purpose ($\text{Output}$).

• Cognitive Space (ConN): Executes actions to achieve Purpose.

• Semantic Space (SemA): Aligns meanings with intended goals.

• Conscious Space: Reflects on Purpose, ensuring alignment with values.

• Conceptual Space (ConC): May update concepts of time management and priorities.

Understanding how the four spaces interact and transform is crucial for a comprehensive cognitive model.

• Concepts in ConC are given meaning through associations in SemA.

• SemA provides the semantic content that makes concepts meaningful.

• New Concepts Formation: ConC can form new concepts based on semantic relationships in SemA.

• Introducing "Electric Vehicle":

• ConC: Combines concepts "Vehicle" and "Electric Power."

• SemA: Provides semantic associations like "zero emissions," "battery-powered."

• ConN processes inputs using structures in ConC.

• ConC provides the framework for understanding and reasoning.

• Updating Concepts: Cognitive functions in ConN can update or refine concepts in ConC based on new experiences.

• Learning a New Language:

• ConN: Processes new linguistic inputs.

• ConC: Updates language-related concepts and vocabulary.

• SemA guides ConN in interpreting and generating meaningful content.

• ConN relies on semantic associations to make sense of inputs.

• Modifying Semantics: Cognitive processes in ConN can modify semantic associations in SemA.

• Correcting a Misunderstanding:

• ConN: Realizes that "bank" can mean a financial institution or riverbank.

• SemA: Updates semantic associations to reflect multiple meanings.

• Conscious Space monitors and regulates activities in ConN, ConC, and SemA.

• Provides self-awareness and higher-order cognition.

• Deliberate Changes: Conscious reflections can lead to changes in concepts, cognitive processes, and semantic associations.

• Ethical Reflection:

• Deciding to adopt a vegetarian diet after reflecting on animal welfare.

• Conscious Space: Reflects on values.

• ConC: Updates concepts related to food choices.

• SemA: Strengthens associations between "meat" and "ethical concerns."

• Purpose drives transformations across all spaces.

• Ensures that cognitive activities are goal-directed and aligned with values.

• Pursuing a Career Goal:

• Purpose: Become a doctor.

• ConN: Engages in learning activities.

• ConC: Builds medical knowledge concepts.

• SemA: Forms strong semantic associations in medical terminology.

• Conscious Space: Maintains motivation and self-awareness.

The framework mirrors human cognitive development stages:

1. Perceptual Stage:

• Function: Recognize sensory inputs without assigned meanings.

• Spaces Involved: ConN processes raw data.

2. Conceptual Stage:

• Function: Associate sensory inputs to form basic concepts.

• Spaces Involved: ConC structures initial concepts; SemA begins to assign meanings.

3. Relational Stage:

• Function: Understand relationships and patterns between concepts.

• Spaces Involved: SemA builds semantic networks; ConN processes relationships.

4. Abstract Stage:

• Function: Develop higher-level reasoning and abstraction.

• Spaces Involved: ConC organizes complex concepts; ConN engages in abstract thinking; Conscious Space emerges.

• Progressive Learning:

• AI systems start with basic recognition tasks and progressively build complexity.

• Feedback Mechanisms:

• Implement mechanisms to detect inconsistencies ("bugs") and promote learning.

• Adaptive Algorithms:

• Use machine learning techniques to evolve semantic representations over time.

• Conscious Processing:

• Deliberate reasoning in ConN and Conscious Space.

• Example: Solving a complex problem step by step.

• Subconscious Processing:

• Implicit understanding influencing ConN operations.

• Example: Instinctively recognizing a face without conscious effort.

• Definition:

• Inconsistencies ("bugs") in reasoning prompt cognitive growth.

• Mechanisms in AI:

• Error Detection: Systems identify contradictions or gaps in understanding.

• Error Correction: Adjust semantic representations to resolve inconsistencies.

• Learning: Use inconsistencies as opportunities to refine models.

• Constructs Emerge from Semantics:

• Mathematical forms are derived from underlying semantics.

• Semantic Equations:

• Equations explicitly represent semantic relationships.

• Semantic Functions:

• Functions map entities to their semantic representations.

• Semantic Sets:

• Sets defined by shared semantic attributes.

• Categories:

• Groupings based on semantic relationships and hierarchies.

• Semantic Functions and Mappings:

• Account for semantics of domain and codomain elements.

1. Perceptual Stage (ConN):

• Recognize sensory inputs: trunk, branches, leaves.

2. Conceptual Stage (ConC):

• Form the concept "tree" by aggregating features.

• AGG(etrunk,ebranches,eleaves)=etree\text{AGG}(e_{\text{trunk}}, e_{\text{branches}}, e_{\text{leaves}}) = e_{\text{tree}}AGG(etrunk​,ebranches​,eleaves​)=etree​

3. Relational Stage (SemA):

• Understand relationships: "trees provide shade," "trees absorb CO₂."

• Semantic associations between "tree" and "environmental benefits."

4. Abstract Stage (ConN and Conscious Space):

• Generalize to various types of trees.

• Form abstract concepts like "deciduous trees," "evergreen trees."

• Entities:

• EtreeE_{\text{tree}}Etree​

• Attributes:

• A={atrunk,abranches,aleaves}A = \{ a_{\text{trunk}}, a_{\text{branches}}, a_{\text{leaves}} \}A={atrunk​,abranches​,aleaves​}

• Relations:

• R={rprovide(Etree,Eshade),rabsorb(Etree,ECO₂)}R = \{ r_{\text{provide}}(E_{\text{tree}}, E_{\text{shade}}), r_{\text{absorb}}(E_{\text{tree}}, E_{\text{CO₂}}) \}R={rprovide​(Etree​,Eshade​),rabsorb​(Etree​,ECO₂​)}

• Semantic Network:

• Nodes: "Tree," "Shade," "CO₂."

• Edges: Relationships indicating actions or properties.

• Word "Virus":

• CS("virus",Ccomputing)=Emalware\text{CS}("virus", C_{\text{computing}}) = E_{\text{malware}}CS("virus",Ccomputing​)=Emalware​

• CS("virus",Cmedical)=Epathogen\text{CS}("virus", C_{\text{medical}}) = E_{\text{pathogen}}CS("virus",Cmedical​)=Epathogen​

• Medical Context (CmedicalC_{\text{medical}}Cmedical​):

• Computing Context (CcomputingC_{\text{computing}}Ccomputing​):

• Process:

• Determine context based on surrounding information.

• Select appropriate semantic association.

• Email Filtering AI:

• Encounters the word "virus."

• Uses context to decide whether it's medical advice or a warning about a computer virus.

• Adjusts response accordingly.

The modified DIKWP framework, integrated with the four spaces, addresses the paradox by:

• Emphasizing Semantics: Ensures that mathematical constructs are grounded in real-world meanings.

• Modeling Human Cognition: Reflects the stages of cognitive development, enabling AI to build understanding progressively.

• Integrating Cognitive Processes: Incorporates conscious and subconscious reasoning, acknowledging the human element.

• Prioritizing Purpose: Embeds goal-oriented processing, aligning actions with objectives and values.

• Enhancing Interactions: Facilitates dynamic interactions among the four spaces, mirroring the complexity of human cognition.

• Enhanced Understanding:

• AI systems comprehend language with deeper semantic awareness.

• Contextual Interpretation:

• Improved ability to interpret meaning based on context.

• Human-Like Reasoning:

• AI systems emulate human cognitive processes.

• Adaptive Learning:

• Continuous learning and adaptation based on new information.

• Semantic Ontologies:

• Rich, semantically grounded ontologies that accurately represent domains.

• Interoperability:

• Facilitate communication between systems through shared semantics.

• Inference Engines:

• AI systems draw logical conclusions based on semantic relationships.

• Problem Solving:

• Enhanced capability to address complex problems through semantic reasoning.

• Natural Communication:

• Interfaces that understand and respond to human semantics.

• Personalization:

• Tailored experiences based on individual semantic profiles.

• Human-AI Collaboration:

• Systems that work alongside humans, enhancing productivity and decision-making.

• Shared Understanding:

• Common semantic frameworks facilitate effective collaboration.

By renewing the operations on the DIKWP model based on Prof. Duan's modified framework and integrating the four spaces, we align mathematical constructs with real-world semantics and human cognitive processes. This approach addresses the paradox in traditional mathematics regarding AI semantics and advances the development of AI systems with genuine semantic understanding.

Key Contributions:

• Evolutionary Construction:

• Reflects human cognitive development, ensuring AI systems build understanding progressively.

• Integration of Cognitive Processes:

• Incorporates conscious and subconscious reasoning.

• Semantic Prioritization:

• Ensures mathematical constructs are meaningful and applicable.

• Dynamic Interactions:

• Facilitates complex cognitive processing through interactions among ConC, ConN, SemA, and Conscious Space.

Implications for AI Development:

• Enhanced Understanding:

• AI systems achieve deeper comprehension, mirroring human understanding.

• Improved Interaction:

• Facilitates natural and meaningful human-AI interactions.

• Advancement of Knowledge Representation:

• Offers robust frameworks for representing and reasoning about knowledge.

• 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. ".

• Duan, Y. (2024). Standardization of DIKWP Semantic Mathematics of International Test and Evaluation Standards for Artificial Intelligence based on Networked Data-Information-Knowledge-Wisdom-Purpose (DIKWP) Model. DOI: 10.13140/RG.2.2.26233.89445