机器思维的数学原理  

Mathematical Principles of Machine Thinking

作　　者：朱平 邹卫明 吕珀华 史进 蒋学涛 马益荣 ZHU Ping;ZOU Weiming;LYU Pohua;SHI Jin;JIANG Xuetao;MA Yirong(Beijing Broad Network&Information Company Limited,Beijing 101111,China;Tellhow Institute of Smart City,Beijing 100176,China;Beijing Tellhow Intelligent Engineering Company Limited,Beijing 100176,China)

机构地区：[1]北京博大网信股份有限公司,北京101111 [2]泰豪智慧城市研究院,北京100176 [3]北京泰豪智能工程有限公司,北京100176

出　　处：《计算机科学》2024年第S01期1055-1062,共8页Computer Science

摘　　要：本研究以构建以人类可以理解的方式寻找解决实际问题的方法与步骤的机器思维机制为目的。数学是人类描述客观世界状态和运行规律的重要思维工具。数学也是机器类人自动求解问题答案、解释运行方法和生成中间步骤的重要工具。客观世界的描述语言表述形式多样、规模巨大且特征稀疏,其语义表示、语义积聚、语义分析、以及机器思维机制的实现方法都是基于用例积累渐进式明晰和完善的。在数学应用题类人自动求解领域,机器思维主要依靠的基本数学概念及其蕴含的计算理论包括集合、比例(分数)、不等关系、枚举和数据归纳与推导(趋势判别)等。从机器思维系统实现的角度,以集合对象及其比例计算的语义渐进积聚和识别为例,讨论了数学原理在机器思维系统中的应用技术路线。最后,用示例介绍了机器自动类人求解一道具体的初等数学应用题的完整过程和中间步骤,展望了机器思维应用不等关系、枚举、数轴、坐标系和数学归纳与推导等数学工具的方法和前景。Constructing machine thinking mechanisms that are understandable to humans is the ultimate goal of this paper.Ma-thematic is an important thinking tool for humans to describe the state and running laws of the objective world,and is also a tool for machines to automatic resolving,interpretable running,and intermediate steps generating.The description language of the objective world has diverse forms,huge scale,and sparse features.Its semantic representation,semantic accumulation,semantic analyzing,and the implementation of machine thinking mechanisms are all based on progressive clarity and perfection by use cases.In the field of automatic humanoid solving elementary mathematic application problem,machine thinking mainly relies on basic mathematical concepts and their underlying computation theories,including set,proportion(fraction),unequal relationship,enumeration,and data induction and derivation(trend discrimination).Taking the semantic gradual accumulation and recognition of set elements and their proportions as the example,this paper discusses the application technology of mathematical principles in machine thinking systems from the perspective of machine thinking system implementation.Finally,an example is presented to illustrate the complete process and intermediate steps of machine automated humanoid resolving a specific elementary mathematic application problem.The methods and prospects of using mathematical tools such as inequality,enumeration,number axis,coordinate system,and mathematical induction and deduction in machine thinking are discussed.

关 键 词：机器思维 集合 比例 数学对象 数学概念 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]