Essence Computation and Reasoning (ESCR)

Yucong Duan

Benefactor: Shiming Gong

AGI-AIGC-GPT Evaluation DIKWP (Global) Laboratory

DIKWP-AC Artificial Consciousness Standardization Committee

World Conference on Artificial Consciousness

World Artificial Consciousness Association

(Email：duanyucong@hotmail.com)

Catalog

1 Key concepts

2 The Implementation Process of ESCR

3 Specific case analysis

3.1 ESCR Implementation of Goldbach Conjecture

3.2 ESCR Implementation of Collatz Conjecture

4 Conclusion

References

Essence Computing and Reasoning (ESCR) is a method of reasoning and computing from a semantic perspective by identifying and analyzing the essential characteristics and their combination relationships of things. ESCR is based on a series of essential axioms and inference rules, aiming to reveal the deep semantic relationships of complex systems and problems, and provide new explanations for mathematical and logical problems.

1 Key concepts

Consistency of Compounded Essential Set Axiom, CES:

Any type of essential set must maintain consistency and completeness when combined, that is, essential characteristics cannot lose their original semantics during the combination process.

Mathematical expression:

CES(ASS(A)):=ASS(CES(A))

Definition of Essence Attributes:

Identify and define the essential attributes of things, which play a crucial role in semantic reasoning and computation processes.

Mathematical expression:

ESS(A):={a₁,a₂,…,a_n}

Combination Rules of Essence Attributes:

The essential attributes follow specific rules in the combination process to ensure consistency and integrity of the combined whole.

Mathematical expression:

ASS(ESS(A),ESS(B)):=ESS(ASS(A,B))

2 The Implementation Process of ESCR

Identify essential attributes:

Determine the essential attributes of things, which are the core features of things in semantic space.

For example, in Goldbach's conjecture, the essential properties of even numbers E and prime numbers P can be defined as their numerical properties and combinatorial relationships.

Define essential attribute combination rules:

Determine the rules for essential attributes in the combination process to ensure consistency and completeness of the overall composition.

For example, in Goldbach's conjecture, the combination of two prime numbers P must satisfy that their sum is equal to an even number E.

Perform essential calculations and reasoning:

By applying CES and essential attribute combination rules, the deep semantic relationships of the problem are revealed through the combination and inference of essential attributes.

For example, deriving the semantic interpretation of Goldbach's conjecture through essential computation and inference (ESCR).

3 Specific case analysis

3.1 ESCR Implementation of Goldbach Conjecture

The definition of Goldbach's conjecture:

Any even number greater than 2 can be represented as the sum of two prime numbers.

Identify essential attributes:

The essential properties of even number E include its numerical properties and its properties as the sum of two prime numbers.

Mathematical expression:

ESS(E):={Numerical properties, as the sum of two prime numbers}

Define essential attribute combination rules:

The combination of two prime numbers P must satisfy that their sum is equal to an even number E.

Mathematical expression:

ASS(ESS(P₁),ESS(P₂)):=ESS(E)

Perform essential calculations and reasoning:

By essential computation and inference (ESCR), it is determined that the even number E can be represented as the sum of two prime numbers P.

Mathematical expression:

ESS(E):=ASS(ESS(P₁),ESS(P₂))=>P₁+P₂=E

3.2 ESCR Implementation of Collatz Conjecture

The definition of the Collatz conjecture:

For any positive integer n, if n is odd, calculate 3n+1; If n is an even number, calculate n/2. This loop will eventually return to 1.

Identify essential attributes:

The essential properties of natural number N include its parity and related operation rules.

Mathematical expression:

ESS(N):={Parity, operation rules}

Define essential attribute combination rules:

The combination rules of odd O and even E include the application of their operation rules.

Mathematical expression:

ASS(ESS(O),ESS(E)):={3O+1,E/2}

Perform essential calculations and reasoning:

The process of deducing the natural number N will eventually return to 1 through essential computation and inference (ESCR).

Mathematical expression:

ESS(N):=ASS(ESS(O),ESS(E))=>{3O+1,E/2}=>N→1

4 Conclusion

Essentially Computational and Reasoning (ESCR) provides a new perspective to understand the deep semantic relationships of complex systems and problems by identifying and analyzing the essential attributes and their combination relationships of things, and conducting reasoning and calculations from a semantic perspective. ESCR is not only applicable to Goldbach's conjecture and Collatz's conjecture, but can also be applied to other mathematical and logical problems, providing new methods and ideas for the study of these problems.

References

[1] Y. Duan. "Towards a Periodic Table of conceptualization and formalization on State, Style, Structure, Pattern, Framework, Architecture, Service and so on." SNPD 2019: 133-138.

[2] Y. Duan. "Existence Computation: Revelation on Entity vs. Relationship for Relationship Defined Everything of Semantics." SNPD 2019: 139-144.

[3] Y. Duan. "Applications of Relationship Defined Everything of Semantics on Existence Computation." SNPD 2019: 184-189.

[4] Y. Duan, S. Xiaobing , C. Haoyang , Chunjie Cao, Zhao Li, Xiaoxian Yang. "Modeling Data, Information and Knowledge for Security Protection of Hybrid IoT and Edge Resources." IEEE Access 7: 99161-99176 (2019).

[5] 段玉聪等, "跨界、跨 DIKW 模态、介尺度内容主客观语义融合建模与处理研究." 中国科技成果，2021年8月498期，45-48.

[6] Y. Duan, "Semantic Oriented Algorithm Design: A Case of Median Selection," 2018 19th IEEE/ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD), 2018, pp. 307-311, doi: 10.1109/SNPD.2018.8441053.

[7] Y. Duan, "A Constructive Semantics Revelation for Applying the Four Color Problem on Modeling," 2010 Second International Conference on Computer Modeling and Simulation, 2010, pp. 146-150, doi: 10.1109/ICCMS.2010.113.

[8] Y. Duan, A dualism based semantics formalization mechanism for model driven engineering, IJSSCI, vol. 1, no. 4, pp. 90-110, 2009.

[9] Y. Duan, "Efficiency from Formalization: An Initial Case Study on Archi3D" in Studies of Computing Intelligence, Springer, 2009.

[10] Y. Duan, "Creation Ontology with Completeness for Identification of 3D Architectural Objects" in ICCTD, IEEE CS press, pp. 447-455, 2009.

[11] Y. Huang and Y. Duan, "Towards Purpose Driven Content Interaction Modeling and Processing based on DIKW," 2021 IEEE World Congress on Services (SERVICES), 2021, pp. 27-32, doi: 10.1109/SERVICES51467.2021.00032.

[12] T. Hu and Y. Duan, "Modeling and Measuring for Emotion Communication based on DIKW," 2021 IEEE World Congress on Services (SERVICES), 2021, pp. 21-26, doi: 10.1109/SERVICES51467.2021.00031.

[13] Y. Duan, Christophe Cruz. "Formalizing Semantic of Natural Language through Conceptualization from Existence." International Journal of Innovation, Management and Technology, 2011, 2 (1), p. 37-42, ISSN: 2010-0248.

[14] Y. Duan, "A stochastic revelation on the deterministic morphological change of 3x+1," 2017 IEEE 15th International Conference on Software Engineering Research, Management and Applications (SERA), 2017, pp. 333-338, doi: 10.1109/SERA.2017.7965748.

[15] Y. Duan, "The end of 'Objective' mathematics as a return to 'Subjective'." February 2022.DOI: 10.13140/RG.2.2.36171.87841.