Elaboration of DIKWP Semantic Mathematics (Computational Science)

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)

Abstract

This report provides a detailed exposition of the DIKWP Semantic Mathematics (Computational Science) framework, which mathematically formalizes the components of Data, Information, Knowledge, Wisdom, and Purpose (DIKWP). This framework emphasizes objective sameness, objective difference, and objective completeness through rigorous computational methods. It assumes the availability of ample, precise, and consistent data, enabling exhaustive analysis and logical inference to ensure comprehensive coverage and no omissions within the knowledge structure. This approach is particularly suited for applications demanding high precision and verifiability, distinguishing it from the alternative version based on Professor Duan Yucong's "Consciousness Bug" theory, which incorporates abstraction, hypothesis, and simplification to handle incomplete and uncertain information.

1. Introduction and Motivation

1. Overview of the DIKWP FrameworkThe DIKWP framework is a model used to describe cognitive and information processing mechanisms, comprising five core components:

• D (Data): Emphasizes the recognition of "sameness" attributes.

• I (Information): Derives useful information by analyzing "differences" between data points.

• K (Knowledge): Forms a "complete" semantic network through the integration of information.

• W (Wisdom): Makes decisions based on comprehensive and objective knowledge.

• P (Purpose): Provides clear goal-oriented guidance for the entire processing sequence.

2. Computational Science Version and Its ObjectivesIn this version, the DIKWP framework is situated within an idealized computational science context. It assumes the availability of abundant, precise, and consistent data, which can be exhaustively analyzed. The system strives to understand the target domain comprehensively and objectively across Data, Information, and Knowledge layers, thereby eliminating the need for subjective hypotheses or abstractions during decision-making and goal achievement. This version ensures maximum logical rigor, determinism, and verifiability.

2. Core Principles of DIKWP Semantic Mathematics (Computational Science)

1. Objective SamenessAt the data level, "sameness" refers to a set of elements sharing strictly consistent attributes across specified dimensions. A similarity function Sobj(di)S_{\text{obj}}(d_i)Sobj​(di​) precisely quantifies the degree to which elements did_idi​ exhibit uniformity in a particular attribute. When Sobj(di)=ConstantS_{\text{obj}}(d_i) = \text{Constant}Sobj​(di​)=Constant, the elements are deemed objectively identical in that attribute.

2. Objective DifferenceInformation is derived by objectively measuring and identifying differences between data points. The difference function Δobj(di,dj)\Delta_{\text{obj}}(d_i, d_j)Δobj​(di​,dj​) quantifies the precise disparities between any two data points across multiple attribute dimensions. This process relies solely on comprehensive data comparison, ensuring the generated information is thorough and accurate.

3. Objective CompletenessKnowledge aims for "objective completeness," meaning the knowledge network encompasses all possible relational links without logical omissions. This is achieved by exhaustively analyzing data and information to construct a knowledge network Kobj=(N,E)K_{\text{obj}} = (N, E)Kobj​=(N,E), where $N$ represents information elements and $E$ signifies the relationships between them. The closure operation Closure(Kobj)\text{Closure}(K_{\text{obj}})Closure(Kobj​) ensures that the knowledge network fully covers all logically inferable relationships.

3. Component Representations in DIKWP Semantic Mathematics (Computational Science)

1. Data (D): Objective Sameness

   Intent: Objectively identify and quantify the "sameness" between data points, ensuring that all data precisely conform to specified attributes.

   Mathematical Representation:

   Data Operations:

• Intersection ($\cap$): Dobj1∩Dobj2={di∣diD_{\text{obj1}} \cap D_{\text{obj2}} = \{ d_i \mid d_iDobj1​∩Dobj2​={di​∣di​ maintains objective sameness across multiple data sets $\}$.

• Union ($\cup$): Dobj1∪Dobj2={di∣diD_{\text{obj1}} \cup D_{\text{obj2}} = \{ d_i \mid d_iDobj1​∪Dobj2​={di​∣di​ satisfies objective sameness in at least one data set $\}$.

• Similarity Function Sobj(di)S_{\text{obj}}(d_i)Sobj​(di​): Quantifies the degree of similarity in a specific attribute.

• Data Set Dobj={di∣Sobj(di)=Constant}D_{\text{obj}} = \{ d_i \mid S_{\text{obj}}(d_i) = \text{Constant} \}Dobj​={di​∣Sobj​(di​)=Constant}: Defines a data set where all elements exhibit the same quantified similarity in the given attribute.

2. Information (I): Objective Difference

   Intent: Objectively identify and quantify the differences between data points to generate meaningful information. All differences are captured through exhaustive comparisons, ensuring no disparities are overlooked.

   Mathematical Representation:

   Information Operations:

• Difference Calculation: Δobj(di,dj)=∣Sobj(di)−Sobj(dj)∣\Delta_{\text{obj}}(d_i, d_j) = |S_{\text{obj}}(d_i) - S_{\text{obj}}(d_j)|Δobj​(di​,dj​)=∣Sobj​(di​)−Sobj​(dj​)∣, where differences are calculated across one or more attributes.

• Classification: Information is categorized based on specific attributes that define objective differences.

• Difference Function Δobj(di,dj)\Delta_{\text{obj}}(d_i, d_j)Δobj​(di​,dj​): Measures the precise difference between two data points across specific attributes.

• Information Set Iobj={Δobj(di,dj)∣di,dj∈Dobj}I_{\text{obj}} = \{ \Delta_{\text{obj}}(d_i, d_j) \mid d_i, d_j \in D_{\text{obj}} \}Iobj​={Δobj​(di​,dj​)∣di​,dj​∈Dobj​}: Represents all quantified differences derived from the data set.

3. Knowledge (K): Objective Completeness

   Intent: Construct a knowledge network that achieves "objective completeness" by fully encompassing all potential relational links derived from the information set.

   Mathematical Representation:

   Knowledge Operations:

• Network Construction: Systematically build KobjK_{\text{obj}}Kobj​ by analyzing and integrating all elements of IobjI_{\text{obj}}Iobj​.

• Expansion: Incorporate new information by updating KobjK_{\text{obj}}Kobj​ to maintain completeness as additional data becomes available.

• Knowledge Network Kobj=(N,E)K_{\text{obj}} = (N, E)Kobj​=(N,E): $N$ represents information elements, and $E$ denotes the relationships between these elements.

• Closure Operation Closure(Kobj)\text{Closure}(K_{\text{obj}})Closure(Kobj​): Ensures that the knowledge network includes all logically inferable relationships within the information set.

4. Wisdom (W): Objective Decision Making

   Intent: Utilize the comprehensive and objective knowledge network to inform decision-making processes, ensuring that all decisions are based on thorough and unbiased analysis.

   Mathematical Representation:

• Wisdom Function Wobj(Kobj)W_{\text{obj}}(K_{\text{obj}})Wobj​(Kobj​): Applies the complete knowledge network to make logical and fact-based decisions.

• Example: In a medical context, WobjW_{\text{obj}}Wobj​ might use KobjK_{\text{obj}}Kobj​ to diagnose a condition accurately based on comprehensive medical data.

5. Purpose (P): Objective Goal Achievement

   Intent: Guide the system's operations towards clearly defined objectives, ensuring that the transformation from data to output remains logically rigorous and fully aligned with the intended goals.

   Mathematical Representation:

   Purpose Operations:

• Transformation Function TPT_PTP​: Ensures that the system's outputs are fully consistent with the objectives, relying solely on complete and accurate data and knowledge.

• Purpose Tuple Pobj=(Input,Output)P_{\text{obj}} = (Input, Output)Pobj​=(Input,Output): Directs the transformation process through a conversion function TP:Input→OutputT_P: Input \rightarrow OutputTP​:Input→Output, ensuring outcomes are precisely aligned with predefined objectives.

4. Feedback and Iterative Improvement

While this version assumes the availability of comprehensive and consistent data, real-world scenarios may involve dynamic data changes. Therefore, the system must incorporate mechanisms to:

• Dynamically Expand the Knowledge Network: When new data is introduced, the system recalculates and updates IobjI_{\text{obj}}Iobj​ and KobjK_{\text{obj}}Kobj​ to maintain completeness.

• Continuous Verification and Refinement: Any new information triggers a closure operation to revalidate and expand KobjK_{\text{obj}}Kobj​, ensuring the knowledge network remains complete and consistent.

This feedback process operates entirely within a strictly logical framework, devoid of subjective hypotheses. By updating the data and information sets, the system automatically reconstructs and verifies the knowledge network's integrity.

5. Applicable Scenarios and Limitations

• Applicable Scenarios:The DIKWP Semantic Mathematics (Computational Science) version is ideal for domains that demand maximum precision and comprehensiveness, such as industrial process control, high-precision scientific computations, rigorously regulated engineering designs, or systems where data quality and coverage are paramount. In these scenarios, the availability of complete and precise data ensures the system can build an exhaustive knowledge structure and make logically sound, objective decisions.

• Limitations:This version faces challenges when data is incomplete, imprecise, or inconsistent. The absence of abstraction or hypothesis mechanisms results in poor adaptability under uncertain conditions. This contrasts with Professor Duan Yucong's "Consciousness Bug" theory-based version, which employs hypothesis, abstraction, and simplification to handle incomplete information, thereby maintaining functionality despite the "3-No problems" (incompleteness, imprecision, inconsistency).

6. Comparison with the Alternative Version (Consciousness "Bug" Theory)

Compared to the alternative DIKWP Semantic Mathematics (Consciousness "Bug" Theory) version:

• Computational Science Version: Emphasizes strict objectivity, thoroughness, and precision, aiming for comprehensive and accurate knowledge generation through exhaustive data analysis and objective reasoning.

• Consciousness "Bug" Theory Version: Emulates human cognitive processes by incorporating abstraction, hypothesis generation, and simplification, allowing flexibility and adaptability in handling incomplete and uncertain information.

These two versions complement each other, with one suited for high-data-quality environments requiring precision and the other adaptable to scenarios with missing or uncertain information, thereby providing a multi-dimensional strategic reference for building more versatile and robust artificial consciousness systems.

7. Conclusion and Outlook

The DIKWP Semantic Mathematics (Computational Science) version offers a rigorous, systematic framework for objectively handling Data, Information, Knowledge, Wisdom, and Purpose. By focusing on completeness and precision, this version ensures that system operations are based on logical consistency and exhaustive analysis, making it highly suitable for applications where accuracy and thoroughness are paramount.

Future Work:

• Hybrid Models: Explore integrating the Computational Science version with the "Consciousness Bug" theory-based version to create a hybrid model that achieves both precision in high-data-quality scenarios and adaptability in information-deficient environments.

• Practical Validation: Apply the framework to specific application domains to empirically test and optimize its performance and limitations in real-world tasks.

Through continuous refinement of the DIKWP Semantic Mathematics framework, we aim to develop more robust artificial intelligence and consciousness systems capable of adapting from idealized data environments to the complex and variable real world, thereby providing theoretical and technical support for innovations in cognition and decision-making.