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 document presents a comprehensive proposal of the Data-Information-Knowledge-Wisdom-Purpose (DIKWP) Semantic Mathematics framework by integrating the composition mechanisms of Ludwig Wittgenstein's logical structure and the philosophical insights of Baruch Spinoza. By unifying Wittgenstein's logical composition in the semantics of Data (D), Information (I), and Knowledge (K) with Spinoza's concepts of Intuitive Knowledge, Ethical Living, and Purposeful Action in Wisdom (W) and Purpose (P), we aim to enhance the DIKWP model. This integrated framework provides a robust mathematical foundation for modeling complex semantic relationships, ethical reasoning, and purposeful actions within artificial intelligence (AI) systems, aligning them with human cognitive processes and values.

1. Introduction

• 1.1. Overview

• 1.2. Objectives

2. Overview of the DIKWP Semantic Mathematics Framework

• 2.1. The DIKWP Model

• 2.2. Integration of Philosophical Insights

3. Integrating Wittgenstein's Logical Composition into DIKWP

• 3.1. Data: Elementary Propositions and Sameness

• 3.2. Information: Logical Composition and Difference

• 3.3. Knowledge: Logical Deduction and Completeness

4. Incorporating Spinoza's Philosophy into DIKWP

• 4.1. Wisdom: Intuitive Knowledge and Ethical Understanding

• 4.2. Purpose: Alignment with Natural Order and Self-Preservation

5. Formalization of the Integrated DIKWP Model

• 5.1.1. Data Level Formalization

• 5.1.2. Information Level Formalization

• 5.1.3. Knowledge Level Formalization

• 5.1.4. Wisdom Level Formalization

• 5.1.5. Purpose Level Formalization

• 5.1. Mathematical Foundations

• 5.2. Examples and Applications

6. Implications for Artificial Intelligence and Cognitive Modeling

• 6.1. Enhanced Semantic Representation

• 6.2. Improved Logical Reasoning and Ethical Decision-Making

• 6.3. Alignment with Human Values and Purposeful Action

7. Challenges and Considerations

• 7.1. Complexity and Computational Feasibility

• 7.2. Maintaining Consistency and Ethical Alignment

8. Conclusion

9. References

The DIKWP model serves as a foundational framework for understanding and modeling cognitive processes, from the acquisition of raw data to purposeful actions guided by wisdom. By integrating the logical composition mechanisms from Wittgenstein's Tractatus Logico-Philosophicus into the semantics of Data, Information, and Knowledge, and incorporating Spinoza's philosophical insights into Wisdom and Purpose, we aim to enrich the DIKWP framework. This integration bridges logical structuring and ethical philosophy, providing a comprehensive model aligned with human cognition and values.

• Propose the DIKWP model by merging previous investigations on Wittgenstein's and Spinoza's contributions.

• Integrate Wittgenstein's logical composition into the semantics of Data, Information, and Knowledge.

• Incorporate Spinoza's philosophy into the semantics of Wisdom and Purpose.

• Formalize the integrated model with mathematical precision.

• Demonstrate the enhanced capabilities of the DIKWP model in AI and cognitive modeling.

The DIKWP model outlines a hierarchical structure of cognitive processing:

1. Data (D): Raw, unprocessed facts characterized by sameness.

2. Information (I): Data processed to highlight differences through relationships and structures.

3. Knowledge (K): Integration of information into a coherent, complete understanding.

4. Wisdom (W): Application of knowledge with ethical considerations and deep understanding.

5. Purpose (P): Guiding motivations and intentions that direct actions and cognitive processes.

• Wittgenstein's Logical Composition:

• Provides mechanisms for composing elementary propositions into complex ones, aligning with the transformation from Data to Information and Knowledge.

• Spinoza's Philosophy:

• Offers insights into intuitive knowledge, ethical living, and purposeful action, enriching the levels of Wisdom and Purpose.

• Elementary Propositions as Data Elements:

• Each data element did_idi​ corresponds to an elementary proposition representing an atomic fact.

• Sameness:

• Data elements share the property of being atomic and indivisible.

• Equivalence Relation ($\sim$): di∼djd_i \sim d_jdi​∼dj​ if did_idi​ and djd_jdj​ represent the same atomic fact.

• Logical Operations:

• Use logical connectives (AND $\wedge$, OR $\vee$, NOT $\neg$) to combine data elements.

• Difference:

• Information arises from the differences and relationships between data elements through logical composition.

• Information Set ($I$):

• $I=\{\varphi \mid \varphi \text{ is a logical combination of elements in }D\}$.

• Knowledge Base ($K$):

• Contains all propositions derived from information through logical deduction.

• Completeness:

• Ensuring that all logical consequences of the information are included.

• Deduction Relation ($⊢$):

• Defines how new propositions are inferred from existing ones.

• Intuitive Knowledge:

• Represents the highest form of understanding, grasping the essence and interconnectedness of all things.

• Wisdom ($W$):

• In the DIKWP model, wisdom involves applying knowledge ethically and holistically.

• Ethical Considerations:

• Actions guided by wisdom are aligned with ethical principles and the natural order.

• Conatus (Striving for Self-Preservation):

• Every being's innate drive to persevere in its existence.

• Purpose ($P$):

• In DIKWP, purpose reflects guiding motivations aligned with self-preservation and the well-being of the whole.

• Alignment with Natural Order:

• Actions are directed in harmony with universal laws and ethical considerations.

• Set of Atomic Data Elements ($D$):

• D={d1,d2,...,dn}D = \{ d_1, d_2, ..., d_n \}D={d1​,d2​,...,dn​}.

• Equivalence Relation ($\sim$):

• di∼djd_i \sim d_jdi​∼dj​ if did_idi​ and djd_jdj​ are identical atomic facts.

• Elementary Propositions (pip_ipi​):

• Each did_idi​ corresponds to an elementary proposition pip_ipi​.

• Logical Connectives:

• $\{\wedge ,\vee ,\neg \}$.

• Information Elements ($I$):

• I={ϕ∣ϕ is a logical composition of pi∈D}I = \{ \phi \mid \phi \text{ is a logical composition of } p_i \in D \}I={ϕ∣ϕ is a logical composition of pi​∈D}.

• Semantic Difference:

• Differences are defined through the structure of logical compositions.

• Knowledge Base ($K$):

• $K=(S,⊢)$, where $S$ is a set of axioms including elementary propositions and $⊢$ is the deduction relation.

• Logical Deduction:

• New propositions are derived using inference rules (e.g., Modus Ponens).

• Completeness and Consistency:

• $\forall \varphi \in \mathbb{L},\varphi \in K\vee \neg \varphi \in K$.

• $⊬\varphi \wedge \neg \varphi$.

• Utility Function ($U$):

• $U:K\to \mathbb{R}$, assigning value to knowledge propositions based on ethical considerations.

• Optimal Understanding ($W$):

• Wisdom is the maximization of utility:W=arg⁡max⁡K′U(K′),W = \arg\max_{K'} U(K'),W=argK′max​U(K′),where K′⊆KK' \subseteq KK′⊆K represents subsets of knowledge applied.

• Ethical Constraints:

• Actions and decisions must satisfy ethical rules $E$.

• Purpose Function ($P$):

• $P:W\to \text{Actions}$.

• Conatus as Objective:

• Purpose function prioritizes actions that support self-preservation and the common good.

• Alignment with Natural Laws ($\mathcal{N}$):

• $\forall a\in \text{Actions},a\models \mathcal{N}$.

• Data Elements:

• d1d_1d1​: "Person A is hungry."

• d2d_2d2​: "Food is available."

• Information Composition:

• ϕ1=d1∧d2\phi_1 = d_1 \wedge d_2ϕ1​=d1​∧d2​: "Person A is hungry AND food is available."

• Knowledge Derivation:

• From ϕ1\phi_1ϕ1​, deduce ϕ3\phi_3ϕ3​: "Person A can eat to satisfy hunger."

• Wisdom Application:

• Evaluate U(ϕ3)U(\phi_3)U(ϕ3​) considering health, ethics (e.g., is the food rightfully theirs?).

• Purpose Alignment:

• If aligned with self-preservation and ethical considerations, action $a$: "Person A eats the food" is taken.

• Logical Coherence:

• Integration of logical composition enhances the semantic structuring of data and information.

• Complex Relationships:

• AI systems can represent and process complex relationships between data elements.

• Deductive Reasoning:

• AI systems can infer new knowledge logically and consistently.

• Ethical AI:

• Incorporating wisdom and purpose enables AI to make decisions aligned with ethical principles.

• Value Alignment:

• AI actions are guided by purposes that reflect human values and the natural order.

• Purposeful Behavior:

• AI systems act with intention and understanding, enhancing their effectiveness and trustworthiness.

• Scalability:

• Managing the computational complexity of logical deductions and utility evaluations.

• Optimization:

• Developing efficient algorithms for maximizing utility under constraints.

• Consistency:

• Ensuring the knowledge base remains free of contradictions.

• Ethical Ambiguities:

• Addressing situations where ethical considerations may conflict.

By merging the investigations into Wittgenstein's logical composition mechanisms and Spinoza's philosophical insights, we have proposed an enriched DIKWP Semantic Mathematics framework. This integrated model enhances the semantics mechanisms at each level, from the logical structuring of data and information to the ethical application of knowledge in wisdom and purpose. The resulting framework provides a robust foundation for AI systems to represent reality, process information, and act purposefully in alignment with human cognitive processes and values.

1. Wittgenstein, L. (1921). Tractatus Logico-Philosophicus. (Various translations).

2. Spinoza, B. (1677). Ethics. (Translated editions available).

3. 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

4. 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. ".

5. Russell, S., & Norvig, P. (2021). Artificial Intelligence: A Modern Approach (4th ed.). Pearson.

6. Floridi, L. (2011). The Philosophy of Information. Oxford University Press.

7. Frege, G. (1892). On Sense and Reference.

8. Hilbert, D., & Ackermann, P. (1928). Principles of Mathematical Logic. Chelsea Publishing.

9. Gärdenfors, P. (2000). Conceptual Spaces: The Geometry of Thought. MIT Press.

10. Tegmark, M. (2017). Life 3.0: Being Human in the Age of Artificial Intelligence. Knopf.

11. Bostrom, N. (2014). Superintelligence: Paths, Dangers, Strategies. Oxford University Press.

Keywords: DIKWP Semantic Mathematics, Wittgenstein, Spinoza, Data, Information, Knowledge, Wisdom, Purpose, Logical Composition, Ethical Philosophy, Artificial Intelligence, Cognitive Modeling.

Note: This document merges the previous investigations into Wittgenstein's logical composition mechanisms and Spinoza's philosophical insights to propose the DIKWP model anew. By integrating these philosophical contributions, the DIKWP framework is enriched, providing enhanced capabilities for modeling cognitive processes, ethical reasoning, and purposeful action in AI systems.

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