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Existence Computation and Reasoning(EXCR) and Essence Computation and Reasoning(ESCR) based revelation of the semantics of point, line and plane

Abstract

From a cognitive perspective in the semantic space, we proposed the revelation of the semantics of point, line and plane based on our proposed Existence Computation and Reasoning(EXCR) and Essence Computation and Reasoning(ESCR) mechanism.
Existence Computation and Reasoning(EXCR) and Essence Computation and
Reasoning(ESCR) based revelation of the semantics of point, line and plane
基于存在计算与推理的(EXCR)与本质计算与推理(ESCR)的点、线、面的语义空间
(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 point, line and plane based on our proposed Existence
Computation and Reasoning(EXCR) and Essence Computation and Reasoning(ESCR)
mechanism.
一个具体的点 p在一个具体的平面 pl 上是一个认知上具体的存在(p,pl)。这里具
体就是具体确定的意思。
一个抽象的点或点的类型 P在一个抽象的平面 PL 上是一个认知上抽象确定的存
(P,PL)
它们分别对应的存在的语义 ex(p,pl)EX(P,PL)分别指代点 pP在平面对应的变
量空间上被合理的具体语义 iSCR 具体充分限制了。这里的限制的意思就是 P/p
PL/pl 之间的语义联系 ASS(P/p, PL/pl)满足具体的语义一致性条件 CS(P/p,
PL/pl)既然平面 PL 也是公理集合定义 AM(PL)的,也就是平面作为语义载体本身
对应的 ASS(PL)也是公理集合 AM(PL)对应的语义在对应语义空间 ASS(TYPE/type,
INS/ins)空间的具体映射,那么平面空间内的一致性语义 CS(AM, PL)维护能且仅能
在对应公理集合的有效作用范围内。
欧式空间观察定理(EOBS):观察坐标 COD 的具体类型层面的等价变换
MT(TYPE(COD(S), COD(T)))不改变被观察对象 OBS 的类型层面的语义 SM(OBS)
由于欧式空间的坐标 COD(S)=COD(XS, YS, ZS)COD(T)=COD(XT, YT, ZT)变换可以
通过加法运算+与乘法运算*完成,而这两种操作都是符合 CS(TYPE/type, INS/ins)
公理的,因而不对任何坐标改变带来 CS(TYPE/type, INS/ins)语义体系的改变。
(SM(EOBS):=CS(AM, EOBS)) AND (MT(TYPE(COD(S), COD(T))):=CS(AM, EOBS))
=>SM(<EOBS, COD(S)>):=CS(AM, EOBS) AND SM(<EOBS, COD(T)>):=CS(AM, EOBS)
=>SM(<EOBS, COD(S)>)=SM(<EOBS, COD(T)>)
在一个具体的欧式坐标空间 COD(X, Y, Z)中,这个空间在语义层面上符合更普遍的
抽象类型 ASS(X, Y, Z)
SM(COD(X, Y, Z)):=INS(ASS(X, Y, Z))
从语义空间的视角重新认识点、线、面之间的相对语义关系:
为了进行语义层面的存在语义计算于推理 EXCR 与面向本质计算与推理 ESCR 的解
释语义 ExpS 的认知实例构建,我们将从语义空间的视角重新认识点、线、面之
间的相对语义关系
在存在语义层面,遵循存在的守恒公理 CEX,合理的 ASS(X, Y, Z)语义上只是关联
了一组互相不能从存在意义上相互影响各自的独立存在语义的变量 X变量 Y
变量 Z
在欧式坐标空间 COD(X, Y, Z)中变量 X、变量 Y和变量 Z的取值空间分别被限定为
实数 R。根据组合一致性公理 CES,本质变量的数量和其组合等价形态中的独立
成分不可少于其本质变量的数量。
因而可以从 COD(X, Y, Z)推论,COD(X, Y, Z)中的任何语义表达目标蕴含的实数域对
应的自由变量数量不能超过 3个。
而更直接的从 ASS(X, Y, Z)推论,ASS(X, Y, Z)中的任何语义表达目标蕴含的自由变
量数量不能超过 3个。严格的对应 ASS(X, Y, Z)整体的任何等价变量空间的语义表
达本质变量必然等于 3个,如有某个对应系统存在多余 3个变量的表达,那将一
定可以被依据语义一致性公理 CS 的操作对该系统整体溯源到更本质的三个变量
的形态。
平面的语义:
对于任意平面 PL,当坐标空间 COD(X, Y, Z)被认知确定时,对应的平面也就可以
被确定语义描述为,ASS(PL, COD(X, Y, Z))
从抽象的推理可以直接得到,任意确定的平面,抛开概念的表面语义,其本质存
在语义范畴只有一个确定的存在语义 exPL
三维空间 3D 可以被直观看作平面 PL 沿着任意实数坐标 R的集合整体{PL}
3D:={(PLR)}
在这样的三维空间中,exPL 的存在意义就是对一个(PLR)对的 R数值 r的存在对
应。
SM(exPL):=SM(3D, exPL)
:=(PL,r)
由于坐标变换的等价性,这个 R等价对应变量 X变量 Y和变量 Z中的任意一个。
为了便于陈述,我们选取 R=Z
从而我们可以得到平面的语义就是在三维空间中确定了一个变量后的两个变量
的语义空间 PL(X, Y)
ASS(PL, COD(X, Y, Z)):= COD(X, Y)
:=PL(X, Y)
:=COD(X, Y, R(r))
线的语义:
在一个平面 COD(X, Y)中当任意直线 L被认知确定时,对应的直线也就可以被确定
语义描述为,ASS(L, COD(X, Y))
从抽象的推理可以直接得到,任意确定的直线,抛开概念的表面语义,其本质存
在语义范畴只有一个确定的存在语义 exL
二维空间 2D 可以被直观看作直线 L沿着任意实数坐标 R的集合整体{L}
2D:={(LR)}
在这样的二维空间中,exL 的存在意义就是对一个(LR)对的 R数值 r的存在对应。
SM(exL):=SM(2D, exL)
:=(L,r)
由于坐标变换的等价性,这个 R等价对应变量 X变量 Y中的任意一个。为了便
于陈述,我们选取 R=Y
从而我们可以得到直线的语义就是在二维空间中确定了一个变量后的一个变量
的语义空间 L(X)
ASS(L, COD(X, Y)):= COD(X)
:=L(X)
:=COD(X, R(r), R(r))
:=COD(X,R(r))
点的语义:
在一个线 COD(X)中当任意点 P被认知确定时,对应的点也就可以被确定语义描
述为,ASS(P, COD(X))
从抽象的推理可以直接得到,任意确定的点,抛开概念的表面语义,其本质存在
语义范畴只有一个确定的存在语义 exP
一维空间 1D 可以被直观看作点 P沿着任意实数坐标 R的集合整体{P}
1D:={(PR)}
在这样的一维空间中,exP 的存在意义就是对一个(PR)对的 R数值 r的存在对
应。
SM(exP):=SM(1D, exP)
:=(P, r)
从而我们可以得到点的语义就是在一维空间中确定了唯一的变量的取值 x对应
的语义空间 P
ASS(P, COD(X)):= COD(x)
:=P(x)
:=COD(R(r), R(r), R(r))
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、DIKW 模态、介尺度内容主客观语义融合建模与处理研
.中国科技成果,2021 8498 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/358607773_The_end_of_Objective
_mathematics_as_a_return_to_Subjective/stats
(16) 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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Method
Full-text available
we believe that subjective semantics is objectively arranged. We'd like to explore a little bit on the usually viewed subjective math from a cognitive perspective in the semantic space. We reveal our intuition and lay the basis of our proposed definitions of: Semantic Computation and Reasoning Comprising Existence Computation and Reasoning, Essence Computation and Reasoning, Purpose Computation and Reasoning towards Resolution of Conceptual Computation and Reasoning.
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