# 基于存在计算(EXCR)与语义计算(ESCR)的关于四色定理的语义空间(SCR)解释

Existence Computation and Reasoning(EXCR) and Essence Computation and Reasoning(ESCR) based Revelation of the Four Color Theorem

Existence Computation and Reasoning(EXCR) and Essence Computation and Reasoning(ESCR) based Revelation of the Four Color Theorem

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 Four Color Theorem based on our proposed Existence Computation and Reasoning(EXCR) and Essence Computation and Reasoning(ESCR) mechanism following our previous revelation of the semantics of point, line and plane.

SM(C):=(CZ,NZ)

:={(c,z)}

:={(cz,nz))}

:={(z(c),z(!c)))}

0条本质存在的线定义的区域实例：

SMD(Z,L={})

=>NUM(Z)=0

=>NUM(SMD0 (C))=NUM(SMD0 (c1))=1

NUM(EXCR(COD(X, Y), {} )):=1

1条本质存在的线定义的区域实例：

Z(PL=COD(X, Y),l1=COD(X,R(ry)) )

:={Z1(PL=COD(X, Y<R(ry))), Z2(PL=COD(X, Y>R(ry)))}

:={Z1, Z2}

2个区域{Z1, Z2}需要用不同颜色标记，对应这个不同语义的SMD1的本质存在就被确认了。SMD1的基本标记需要2个部分对应，我们用色彩{c1,c2}来标记并对应这2个区域。

SMD(Z, L={l1})

=>NUM({Z1, Z2})=2

=>NUM(SMD1 (C))=NUM(SMD1 ({c1,c2}))=2

SMD(ASS(Y<R(ry), Y>R(ry))):=SMD(ASS(c1, c2))

NUM(EXCR(COD(X, Y), {l1} )):=2

2条本质存在的线定义的区域实例：

Z(PL={Z1, Z2},L{l1=COD(X,R(ry)),l2=COD(R(rx),Y)} )

:={Z11=COD(X<R(rx), Y<R(ry)),Z12=COD(X>R(rx), Y<R(ry)),Z21=COD(X<R(rx), Y>R(ry)),Z22=COD(X>R(rx), Y>R(ry))}

:={Z11, Z12, Z21, Z22}

ASS(ASS(X<R(rx), Y<R(ry)),ASS(X>R(rx), Y<R(ry)),ASS(X<R(rx), Y>R(ry)),ASS(X>R(rx), Y>R(ry)) )

:=ASS(R(rx), R(ry))

:=ASS((X<R(rx), X>R(rx)), SMD1)

:=ASS(Z21(X<R(rx), SMD1) ,Z22(X>R(rx), SMD1) )

:=ASS(Z((X<R(rx), X>R(rx)), SMD1)) )

:=ASS(SMD2, SMD1)

SMD(Z, L={l1, l2})

=>NUM(SMD2, SMD1)=NUM(SMD2 ({c1,c2,c3}))=2+1=3

NUM(EXCR(COD(X, Y), {l1, l2} )):=3

3条本质存在的线定义的区域实例：

Z(PL={Z11, Z12, Z21, Z22},L{l1, l2, l3} )

:=Z(PL, l3)

:={Z(PL,ASS(X, Y)< ASS(R(rx), R(ry))) , Z(PL,ASS(X, Y)> ASS(R(rx), R(ry))) }

:={

Z111=COD(X<R(rx), Y<R(ry), ASS(X,Y) < ASS(R(rx), R(ry))),

Z121=COD(X>R(rx), Y<R(ry)), ASS(X,Y) < ASS(R(rx), R(ry))),

Z211=COD(X<R(rx), Y>R(ry)), ASS(X,Y) < ASS(R(rx), R(ry))),

Z221=COD(X>R(rx), Y>R(ry)), ASS(X,Y) < ASS(R(rx), R(ry))),

Z112=COD(X<R(rx), Y<R(ry), ASS(X,Y) > ASS(R(rx), R(ry))),

Z122=COD(X>R(rx), Y<R(ry)), ASS(X,Y) > ASS(R(rx), R(ry))),

Z212=COD(X<R(rx), Y>R(ry)), ASS(X,Y) > ASS(R(rx), R(ry))),

Z222=COD(X>R(rx), Y>R(ry)), ASS(X,Y) > ASS(R(rx), R(ry))),

}

:={{Z111, Z121, Z211, Z221} ,{Z112, Z122, Z212, Z222}}

ASS(R(rx), R(ry))

:=INS(ASS(X, Y), R)

:=R(X, Y)

:=ASS(ASS(X, Y), R(+),R(*))

ASS(R(rx), R(ry))

:=ASS(ASS(X, Y), R(+),R(*))

:=ASS(ESCR(ASS(X, Y), R(*)))

:=ASS(ESCR(ASS(X, Y), R(+)))

:=ASS((X, Y), R(+))

:=INS(X+Y=R(r))

ASS(R(rx), R(ry), ASS(R(rx), R(ry)))

:=ASS(ASS(X,Y) < ASS(R(rx), R(ry))), ASS(X,Y) > ASS(R(rx), R(ry))), ASS(SMD2, SMD1) )

:=ASS(SMD3, ASS(SMD2, SMD1))

SMD(Z, L={l1, l2, l3})

=>NUM(SMD3, SMD2, SMD1)=NUM(SMD3 ({c1,c2,c3,c4}))=3+1=4

NUM(EXCR(COD(X, Y), {l1, l2, l3} )):=4

3条本质存在的线定义的封闭区域ZC

l3

:=ASS( ASS((X, Y), R(+)), {l1, l2})

:=ASS( ASS((X, Y), R(+)), {COD(X,R(ry)), COD(X,R(rx))})

:=ASS( ASS((X, Y), R(+)), {ASS(X,R(ry)), ASS(X,R(rx))})

:=ASS( {(ASS((X, Y), R(+)), {ASS(X,R(ry))), (ASS((X, Y), R(+)), {ASS(X,R(rx)))})

=>INS(ASS(P1,P2))

ASS(ZC, L, LB)=>LB={}

C(ZC):=C(L(x))

4条及更多的线定义的区域实例：

(1) 线L(x)平行于已存在线集合L{l1, l2, l3}中任意一条的情形，可以对应应用定理(rZPL)进行递归，从而否定增加存在意义上的标记色彩需求。

(2) 线L(x)不平行于已存在线集合L{l1, l2, l3}中任意一条的情形，可以对应应用定理定理(rZCO)或定理(rZCI)进行递归，从而否定增加存在意义上的标记色彩需求。

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，20218498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, 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_ TrueFalse_from_Subjective_YesNo_Semantic_based_on_OWA_and_CWA/citations

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