泛逻辑学——逻辑学的大一统理论

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Title:

Universal logic theory: the comprehensive theory of logic

作者:

何华灿¹, 何智涛²

1. 西北工业大学 计算机学院, 陕西 西安 710072;
2. 北京航空航天大学 计算机学院, 北京 100191

Author(s):

HE Huacan¹, HE Zhitao²

1. School of Computer Science, Northwestern Polytechnical University, Xi’an 710072, China;
2. School of Computer Science and Engineering, Beihang University, Beijing 100191, China

关键词:

形式逻辑; 辩证逻辑; 博弈逻辑; 数理逻辑; 人工智能; 泛逻辑学; 统一理论; 柔性逻辑

Keywords:

formal logic; dialectical logic; game logic; mathematical logic; artificial intelligence; universal logic; unified theories; flexible logic

分类号:

TP183

DOI:

10.11992/tis.202311040

摘要:

人工智能80年研究实践证明，不能用传统物质学科范式做指导，需要进行学科范式变革，接受信息学科范式的指导。相应的，作为智能学科基础理论之一的逻辑学，也需要进行逻辑范式变革，由数理形式逻辑主导变革为由数理辩证逻辑主导。本文阐述了数理形式逻辑和数理辩证逻辑的区别和关系，确认两者是对立不充分的统一体，具有相互补充、各司其职的关系，本文提出的泛逻辑学，可以在数理形式逻辑的基础上，逐步把它拓展成为数理辩证逻辑。因为数理形式逻辑（标准逻辑、刚性逻辑）是全面受到“非此即彼性”约束的理想化的基本逻辑，而数理辩证逻辑是面向现实世界的具有“亦此亦彼性”、甚至“非此非彼性”的高级逻辑，基本逻辑是高级逻辑的一个特例，如同代数是微积分的特例一样。泛逻辑的使命就是在基本逻辑基础上，逐步放开某些逻辑因素的“非此非彼性”，引入“亦此亦彼性”、甚至“非此非彼性”，形成各种不同的非标准逻辑或超协调逻辑，这些逻辑都是整个数理辩证逻辑的组成部分。而且研究证明，柔性命题逻辑算子与柔性神经元可以存在一体两面的等价关系，神经网络可以不是黑箱，而具有明确的逻辑含义。最后指出，数理辩证逻辑是一个开放的逻辑体系，其边界可以不断扩张，没有上限。泛逻辑可以全面无死角地支撑智能学科范式变革的需要。

Abstract:

The research practice of artificial intelligence in the past 80 years has proved that it cannot be guided by the traditional material discipline paradigm, but needs to change the discipline paradigm and accept the guidance of the information discipline paradigm. Accordingly, logic, as one of the basic theories of the intelligence discipline, also needs to change its logic paradigm, from mathematical formal logic to mathematical dialectical logic. This paper expounds the difference and relationship between mathematical formal logic and mathematical dialectical logic, affirming that the two are the unity of opposites and insufficiencies, and have the relationship of complementing each other and fulfilling their respective functions. The universal logic proposed in this paper can be gradually expanded into mathematical dialectical logic on the basis of mathematical formal logic. Because mathematical formal logic (standard logic, rigid logic) is an idealized basic logic that is fully constrained by "either-or", and mathematical dialectical logic is a higher-level logic that faces the real world with "this and that" or even "this and that", and basic logic is a special case of higher-level logic, just as algebra is a special case of calculus. The mission of universal logic is to gradually release the "non-this and non-that" of some logical factors on the basis of basic logic, introduce "this and that", or even "non-this and non-that", and form a variety of different non-standard logic or super-coordinated logic, which are part of the whole mathematical dialectical logic. Moreover, it is proved that flexible propositional logic operators and flexible neurons can be equivalent in one body and two sides, and neural networks can not be black boxes, but have clear logical meanings. Finally, it is pointed out that mathematical dialectical logic is an open logic system, its boundary can be expanded continuously, there is no upper limit. The universal logic can support the need of the paradigm change of intelligence discipline comprehensively and without dead Angle.