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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:
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) Yucong Duan, A dualism based semantics formalization mechanism for model
driven engineering, IJSSCI, vol. 1, no. 4, pp. 90-110, 2009.
(9) Yucong Duan, "Efficiency from Formalization: An Initial Case Study on Archi3D"
in Studies of Computing Intelligence, Springer, 2009.
(10) Yucong 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) 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
(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) 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/
358 607773_The_end_of_Objective
_mathematics_as_a_return_to_Subjective/stats
(16) 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
(17) 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
(18) Yucong Duan, Identifying Objective True/False from Subjective Yes/No
Semantic based on OWA and CWA. July 2013. Journal of Computers 8(7)DOI: