DIKWP Semantic Mathematics: A Glance 

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)

Prof. Yucong DuanInternational Standardization Committee of Networked DIKWP for Artificial Intelligence Evaluation (DIKWP-SC)World Artificial Consciousness CIC (WAC)

DIKWP Semantic Mathematics is a comprehensive mathematical framework designed to process and transform content across the five core components of DIKWP: Data (D), Information (I), Knowledge (K), Wisdom (W), and Purpose (P). The aim of the framework is to provide a systematic approach for representing, processing, and transforming DIKWP content while maintaining the semantic integrity and contextual consistency of each element.

• Objectives:

• Provide semantic precision in processing DIKWP content.

• Ensure adaptability to different AI contexts and real-world applications.

• Enable transparent processing in artificial intelligence systems to generate Artificial Consciousness with objectified subjectivity.

• Applications:

• Artificial Consciousness Systems: Creating advanced decision-making systems that handle subjective elements with objective consistency.

• Cognitive Computing: Support for natural language understanding, knowledge reasoning, and automated decision-making.

• Semantic Blockchain Systems: Encoding DIKWP transformations for secure, transparent, and objective semantic records.

Each DIKWP component is semantically defined, and mathematical transformations are developed to ensure content consistency across networked, bidirectional interactions.

• Definition: Raw and unstructured content representing "sameness" (similar or identical properties).

• Mathematical Representation:Let D={d1,d2,…,dn}D = \{d_1, d_2, \dots, d_n\}D={d1​,d2​,…,dn​} represent a set of data points. Data is categorized and grouped based on concrete properties.

• Transformation Function:

• From Data to Information (D → I):TDI(di)=ijT_{DI}(d_i) = i_jTDI​(di​)=ij​, where iji_jij​ represents information derived from data did_idi​.

• Definition: Structured and contextualized content that identifies "differences" between data points.

• Mathematical Representation:I={i1,i2,…,im}I = \{i_1, i_2, \dots, i_m\}I={i1​,i2​,…,im​} represents extracted information sets based on context and relationships.

• Transformation Function:

• From Information to Knowledge (I → K):TIK(ij)=kmT_{IK}(i_j) = k_mTIK​(ij​)=km​, where kmk_mkm​ represents a structured knowledge node derived from information iji_jij​.

• Definition: Coherent, structured, and complete representations of information, organizing content into logical frameworks (e.g., ontologies or knowledge graphs).

• Mathematical Representation:$K=(N,E)$, where $N$ represents knowledge nodes and $E$ represents the relationships between them.

• Transformation Function:

• From Knowledge to Wisdom (K → W):TKW(km)=wnT_{KW}(k_m) = w_nTKW​(km​)=wn​, where wnw_nwn​ is wisdom, applying structured knowledge kmk_mkm​ to decision-making.

• Definition: Application of knowledge to make decisions based on long-term goals and ethical considerations.

• Mathematical Representation:Let W={w1,w2,…,wp}W = \{w_1, w_2, \dots, w_p\}W={w1​,w2​,…,wp​}, representing decisions based on available knowledge.

• Transformation Function:

• From Wisdom to Purpose (W → P):TWP(wn)=GT_{WP}(w_n) = GTWP​(wn​)=G, where $G$ represents the system’s goal or purpose, informed by wisdom wnw_nwn​.

• Definition: The overarching goal or objective that directs actions and decisions within the system.

• Mathematical Representation:$P=G$, where $G$ defines the purpose aligned with the DIKWP components.

• Feedback Loops:Refinement functions ensure ongoing improvement and realignment based on outcomes:FPD(G,O)F_{PD}(G, O)FPD​(G,O), FPI(G,O)F_{PI}(G, O)FPI​(G,O), etc., where outcomes $O$ drive updates to data, information, knowledge, and wisdom.

The DIKWP model operates in a networked manner, where any element can transform into another. This enables complex bidirectional transformations such as:

• K → D (Knowledge generating new data insights).

• W → I (Wisdom influencing the reinterpretation of existing information).

• P → K (Purpose refining knowledge structures).

MDIKWP=(mDDmDImDKmDWmDPmIDmIImIKmIWmIPmKDmKImKKmKWmKPmWDmWImWKmWWmWPmPDmPImPKmPWmPP)M_{DIKWP} = \begin{pmatrix} m_{DD} & m_{DI} & m_{DK} & m_{DW} & m_{DP} \\ m_{ID} & m_{II} & m_{IK} & m_{IW} & m_{IP} \\ m_{KD} & m_{KI} & m_{KK} & m_{KW} & m_{KP} \\ m_{WD} & m_{WI} & m_{WK} & m_{WW} & m_{WP} \\ m_{PD} & m_{PI} & m_{PK} & m_{PW} & m_{PP} \end{pmatrix}MDIKWP​=​mDD​mID​mKD​mWD​mPD​​mDI​mII​mKI​mWI​mPI​​mDK​mIK​mKK​mWK​mPK​​mDW​mIW​mKW​mWW​mPW​​mDP​mIP​mKP​mWP​mPP​​​

• Interpretation: The transformation matrix maps the interactive relationships between DIKWP elements, enabling the seamless flow of semantics between them.

• Concept: A blockchain designed to record semantics instead of merely conceptual data.

• How It Works: Each block in the chain represents a DIKWP transformation (e.g., D → I, I → K), with a unique hash identifying the semantic changes.

• Application: The blockchain can transparently record the progression of content, from raw data through to decisions, ensuring traceability and semantic consistency.

• Goal: Facilitate more effective human-machine communication by encoding the semantic meaning of information.

• How It Works: A semantic communication protocol will interpret and transform natural language input into DIKWP components, enabling machines to understand intent (P) and meaning (I) at a deeper level.

The TRIZ principles can be mapped and integrated into the networked DIKWP transformations, enabling enhanced innovation opportunities, including patentable inventions:

• Invention Example: An AI-driven semantic optimizer based on DIKWP-TRIZ that systematically evaluates incomplete or inconsistent content to propose optimized solutions through structured transformations.

• Challenge: Incomplete, inconsistent, and imprecise DIKWP content requires adaptive semantic transformation systems.

• Solution: The mutual remedy between DIKWP content ensures continuous improvement and adaptive transformation, leading to more efficient decision-making systems for Artificial Consciousness.

The DIKWP Semantic Mathematics framework provides a foundation for creating intelligent systems that can objectify subjective elements such as meaning, intent, and context. This approach allows for scalable, adaptive, and transparent AI systems capable of decision-making aligned with long-term goals. By integrating the DIKWP-TRIZ principles, this framework can drive innovation and generate new patent opportunities across diverse fields.