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Abstract

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.
The end of “Objective” mathematics as a return to “Subjective”
“客观”数学的终结 Or 数学的主观“回归
By Yucong Duan,
DIKW research group, Hainan University
Email: duanyucong@hotmail.com
Abstract: 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.
公理 AM 都代表着被认知认为合理的一种基础假设 HP假设 HP 就是基于一种前
S对一种结果 T的关联的语义的合理性的主观设定 FSUB
HP(S, T):=FSUB(S, T)
所谓基础或者本质,其语义就是在存在意义上没有进一步可以依赖的解释,也就
是不能再简化的最小部分。
AM:=min(HP)
而假设是类型化知识的本质。由公理出发进而构建的推理目的是为了实现对外部
世界的抽象解释。解释 EXP 就是通过构建输入 S与输出 T的关联将相关案例纳入
相关公理的体系。
EXP(<S, T>, AM):=<S(AM), T(AM)>
:=<FSUB(S),FSUB(T)>
:=FSB<S,T>
这一关于公理的理念与《个人知识》一书作者的宏观理念相符,也是对哥德尔不
完备性定理的抽象。然而相关公理的主观来源又往往由于把相关公理作为独立存
在的普遍的事实而被误认为是绝对客观的了。
数学作为一种基于公理知识的形式系统不断的被人们用来构建对实例的解释和
确定实例化的过程。
每一种具体数学 IM 的有效作用空间 EFP 从类型化知识的角度审视只是建立类型
和实例 IIM 之间的一致性 CS 的类型和实例的关联组合 ASS。这种一致性从认知
角度可以被确定为具体的一致性本质语义 ES
对应于类型 TYPE 和类型实例 type 与实例 INS 和实例实例 ins 之间已经假设的任
何确定的合理的类型层面联系(包括公理和定理)ASS(TYPE/type, INS/ins)
ass(TYPE/type, INS/ins)的一致性 CS(TYPE/type, INS/ins)我们提出对应的语义一致
性公理。
语义一致性公理 CS只有当特定联系 ass(TYPE/type, INS/ins)属于 ASS(TYPE/type,
INS/ins )时,具体的联系 ass(type, ins)才是合理的。
具体的描述形式如下:
CS(TYPE/type, INS/ins)::={ASS(TYPE/type, INS/ins ), ass(TYPE/type, INS/ins)}
ES(IM):=CS(IM, IIM)
:={<IM, IIM>}
EFP(IM):=ASS(ES)
:=(CS(<<IM, IIM>, <IIM, IIM>>))*
一直以来总有人尝试基于错误认知的客观化的具体数学 IM 里去寻求本质上非
经通过对应数学的相关公理 AM(IM)客观化的主观问题 SP 的实例化映射 ISP 的解
。我们将解释,由于搜索空间的隔离这种寻找必然是徒劳无果的。
AM(IM):=Min(ASS<EFP>)
:=min(HP(IM))
进行元分析,形式上,从特定数学出发能得到的结论都是能和其公理集合建立一
致性联系的表达。由于相对特定数学的客观假设 HP(IM)与被归为主观问题的问题
前提如果被视为假设 HP(SP)无交集,从而其实例也建立不起来联系,从而无法形
成期待的解释 EEXP
HP(SP)!=HP(IM)
=>
<S(EEXP),T(EEXP)>!=<S(EXP),T(EXP)>
对应与寻求主观问题的解释,在进行推理前应当从本质语义上回溯到基本公理
上,或者在基本公理的层面上进行相关问题假设的匹配,如果相关问题落在特定
数学的公理语义覆盖范围之外,搜索必然是徒然的。而要继续探求这一解释,
找新的公理是一个可能的方案。
由于公理作为特点数学论证的认知基础具有对依托相关公理的实例化论述的独
立的依托意义,以及对相关论述的一致性范围具有本质上的决定意义。
我们将相关公理集合的构建视为对相关关联论述的存在语义计算与推理(SCR
Semantic Computation and Reasoning层面的工作,称之为存在计算与推理EXCR
Existence Computation and Reasoning)。存在计算与推理更多的侧重从认知直觉
和直觉迁移角度形成语义空间(Semantic Space)的表达确定。
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)
在遵从 CS(TYPE/type, INS/ins)的一致性操作(包括推理和计算)过程中本质上的
存在语义集合 EX {ex}只能被组合但不能被否定存在,或者存在语义不会被改
变。
CEX:
EX({ex}, CS(TYPE/type, INS/ins))
::=EX({Computation({ex}), Reasoning({ex}}, CS(TYPE/type, INS/ins))
我们将基于存在计算与推理得到的相关公理集合的解决具体问题前的类型语义
层面实例化溯源、表达权衡、表达转换、表达迁移和效率优化视为对相关关联论
述的存在语义层面的工作,称之为本质计算与推理(ESCR, Essential Computation
and Reasoning)。
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
(CES, Consistency of Compounded Essential Set)
在遵从 CS(TYPE/type, INS/ins)的一致性操作(包括推理和计算)过程中,本质上
的存在语义集合 EX {ex}的某个具体整体 ISM(CS(EX))的组合 Complex(CS(EX))
多种遵循一致性公理 CS(TYPE/type, INS/ins)的表达形态 Complex(CS(EX))
Complex(T), 这些表达形态之间具有本质语义上的等价性,或者说它们都可以通
过符合 CS(TYPE/type, INS/ins)的一致性操作被规约为 SM(CS(EX))
CES:
ISM(CS(EX))::=ISM(Complex(CS(EX)))
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
.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.
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Method
Full-text available
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.
Method
Full-text available
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