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https://www.researchgate.net/publication/358637942_Existence_Computation_and_ReasoningEXCR_and_Essence_Computation_and_ReasoningESCR_based_Revelation_of_the_Goldbach's_conjecture

Existence Computation and Reasoning(EXCR) and Essence Computation and Reasoning(ESCR) based Revelation of the Goldbach's conjecture

• February 2022

• DOI: 

• 10.13140/RG.2.2.23213.77281

• Projects: 

• From Existence Computation to Semantic Computation through Frequency Defined Fully Typed Resources

• 2021 Data, Information, Knowledge and Wisdom Conference (DIKW 2021)

• Yucong Duan

Existence Computation and Reasoning(EXCR) and Essence Computation and Reasoning(ESCR) based Revelation of the Goldbach's conjecture

基于存在计算(EXCR)与语义计算(ESCR)的关于Goldbach's conjecture的语义空间(SCR)解释

By Yucong Duan,

DIKW research group, Hainan University

Email: duanyucong@hotmail.com

Abstract: From a cognitive perspective in the semantic space, we proposed the revelation of the semantics of the Goldbach's conjecture based on our proposed Existence Computation and Reasoning(EXCR) and Essence Computation and Reasoning(ESCR) mechanism following our previous revelation of the semantics axioms of Conservation of Existence Set (CEX ) and Consistency of Compounded Essential Set (CES).

Goldbach's conjecture的语义解释：

(a)Goldbach's conjecture语义可以从类型的实例的语义角度等价于:

从类型语义的实例层面任何一个偶数E的实例INS(E)=e都可以数值相等对应素数类型P的两个实例INS(P)=p1和INS(P)=p2的数值相加。

INS(E)

:=ASS((INS(P),INS(P)),REL(+))

:=INS(P)+INS(P)

=>e=p1+p2

(b)Goldbach's conjecture语义可以从实例的整体类型的语义角度等价于:

从实例的整体类型语义的层面任何一个偶数E的实例TYPE(INS(E))=E都可以在确认自身的存在语义的基础上，由跨类型的实例层面的关联语义，根据存在计算与推理EXCR的基础假设公理就是存在的守恒公理(CEX, Conservation of Existence Set)等价推导出类型层面的对应语义关联。偶数类型E由于可以通过类型层面语义关联E(x):=R(y)+R(y)建立与自然数类型Z的存在语义关联，从而可以依托存在计算与推理EXCR的基础假设公理存在的守恒公理CEX确定偶数E的类型的依托自然数类型Z的存在语义。

INS(E):=ASS((INS(Z),INS(Z),REL(+))

=>TYPE(E):=ASS((TYPE(Z),TYPE(Z)) ,REL(+))

=>TYPE(E):=ASS(TYPE(Z),REL(+))

=>E:=ASS(Z,REL(+))

=>INS(E):=INS(Z)+INS(Z)

类似的可以通过素数类型P与自然数类型Z之间的类型层面语义关联表达，素数P无法被除了1和它自身外的其他自然数整除(等价于由其它自然数相乘(*)获得):

P=ASS(Z, !(*))

语义表达ASS(Z, !(*))是纯类型层面且其语义表达不需要使用自身P的类型语义存在性，因而可以依托存在计算与推理EXCR的基础假设公理存在的守恒公理CEX确定P的类型层面的存在语义。

在确认了素数P的类型层面存在语义基础上，进而可以使用本质计算与推理ESCR的基础假设公理就是本质集合整体完整性的组合一致性公理(CES, Consistency of Compounded Essential Set)依据素数P的实例INS(P)与自然数类型Z的实例INS(Z)之间的语义关系ASS(P, Z)的具体语义关系，通过类型与实例层面的映射建立对应的类型层面的语义关系。最终得到Goldbach's conjecture的类型语义P+P=E。

ASS(P, Z)

:=ASS(P, TYPE(Z))

:=ASS(P, E)

:=TYPE(ASS(INS(P), INS(E)))

:=TYPE(INS(P)+INS(P)=INS(E)))

:=ASS()

:=P+P=E

注：类似的对应素数P的合数C的语义是C=ASS((Z, Z), (*))。应用CES和CEX可以得到，

C=ASS((Z, Z), (*))=ASS((Z, Z), (+))

但不能得到C=ASS((P, P), (*))，这是由于合数的类型不是本质语义存在，因为合数的自身语义定义用到了更高层面的涵盖其自身的类型的语义的存在性。不能逆着语义范围大小逆向建立语义的存在性依赖关系是对axioms of Conservation of Existence Set (CEX ) and Consistency of Compounded Essential Set (CES)的补充。

综上，我们展示了基于存在计算(EXCR)与语义计算(ESCR)的关于Goldbach's conjecture的语义空间(SCR)解释。

References:

(1) Yucong 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) Yucong Duan: Existence Computation: Revelation on Entity vs. Relationship for Relationship Defined Everything of Semantics. SNPD 2019: 139-144

(3) Yucong Duan: Applications of Relationship Defined Everything of Semantics on Existence Computation. SNPD 2019: 184-189

(4) Yucong Duan, Xiaobing Sun, Haoyang Che, Chunjie Cao, Zhao Li, Xiaoxian Yang:

(5) Modeling Data, Information and Knowledge for Security Protection of Hybrid IoT and Edge Resources. IEEE Access 7: 99161-99176 (2019)

(6) 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

(7) 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.

(8) 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.

(9) Yucong Duan, A dualism based semantics formalization mechanism for model driven engineering, IJSSCI, vol. 1, no. 4, pp. 90-110, 2009.

(10) Yucong Duan, "Efficiency from Formalization: An Initial Case Study on Archi3D" in Studies of Computing Intelligence, Springer, 2009.

(11) Yucong Duan, "Creation Ontology with Completeness for Identification of 3D Architectural Objects" in ICCTD, IEEE CS press, pp. 447-455, 2009.

(12) 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.

(13) 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.

(14) Duan Yucong, Christophe Cruz. Formalizing Semantic of Natural Language through Conceptualization from Existence. International Journal of Innovation, anagement and Technology, 2011, 2 (1), p. 37-42, ISSN: 2010-0248. ffhal-00625002

(15) 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.

(16) Yucong Duan, The end of "Objective" mathematics as a return to "Subjective"

February 2022.DOI: 10.13140/RG.2.2.36171.87841   https://www.researchgate.net/publication/358607773_The_end_of_Objective _mathematics_as_a_return_to_Subjective/stats

(17) Yucong Duan, Existence Computation and Reasoning(EXCR) and Essence Computation and Reasoning(ESCR) based revelation of the semantics of point, line and plane. February 2022

https://www.researchgate.net/publication/358608122_Existence_Computatio n_and_ReasoningEXCR_and_Essence_Computation_and_ReasoningESCR_base d_revelation_of_the_semantics_of_point_line_and_plane

(18) Yucong Duan, Existence Computation and Reasoning(EXCR) and Essence Computation and Reasoning(ESCR) based Revelation of the Four Color Theorem. February 2022

https://www.researchgate.net/publication/358608147_Existence_Computatio n_and_ReasoningEXCR_and_Essence_Computation_and_ReasoningESCR_base d_Revelation_of_the_Four_Color_Theorem

(19) Yucong Duan, Identifying Objective True/False from Subjective Yes/No Semantic based on OWA and CWA. July 2013. Journal of Computers 8(7)

DOI: 10.4304/jcp.8.7.1847-1852

https://www.researchgate.net/publication/276240420_Identifying_Objective_ Tr ueFalse_from_Subjective_YesNo_Semantic_based_on_OWA_and_CWA/citatio ns

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