因素表示的信息空间与广义概率逻辑  

Factorial information space and generalized probability logic

作　　者：汪培庄 周红军 何华灿[3] 钟义信[4] WANG Peizhuang;ZHOU Hongjun;HE Huacan;ZHONG Yixin(Institute of Intelligence Engineering and Math,Liaoning Technical University,Fuxin 123000,China;College of Mathematics,Shannxi Normal University,Xi’an 710062,China;School of Computer Science,Northwestern Polytechnical University,Xi’an 710072,China;Center for Intelligent Science and Technology,Beijing University of Posts Telecommunications,Beijing 100876,China)

机构地区：[1]辽宁工程技术大学智能工程与数学研究院,辽宁阜新123000 [2]陕西师范大学数学学院,陕西西安710062 [3]西北工业大学计算机学院,陕西西安710072 [4]北京邮电大学智能科学技术中心,北京100876

出　　处：《智能系统学报》2019年第5期843-852,共10页CAAI Transactions on Intelligent Systems

基　　金：国家自然科学基金(61350003,60273087,60873001)

摘　　要：国内外近年来所提出的广义概率逻辑对于人工智能的发展有重要意义。能否反映变换演化的实际场景,使逻辑判断能够灵活变通,这是广义概率逻辑发展的关键。为了解决这一问题,本文的目是以信息空间作为逻辑与实际场景的接口。有了这个接口,逻辑判断就能反映变幻莫测的实际场景。本文的方法是用因素空间来定义表现论域以形成新的信息空间,将谓词中的变元取为因素,在已有的逻辑系统中加上本文所提出的背景公理,所有的推理都是在一定背景之下的推理,不同的背景会推出不同的结论。结果是新的逻辑既能维系Stone表示定理的表现要求,又能变得更加灵活有效。结论能使广义概率逻辑更有效地服务于人工智能。为了配合机制主义人工智能的需要,本文还特别提出了语法-语用对接的方法和目标驱动的逆向推理设想,最后为泛逻辑的3种连续算子对进行了数学证明。The generalized probabilistic logic proposed in recent years is of great significance to the development of artificial intelligence.Make flexible judgment that reflects the scene of actual transformation and evolution is the key to the development of the generalized probability logic.Considering this,this paper takes the information space as the interface between logic and actual scene.With this interface,logical judgment can reflect unpredictable real situations.The method in this paper is to use factors space to define the representation domain to form the information space.Then predicate variables are taken as factors,and background axioms are added into the existing logic system.Reasoning is taken under a certain background,different backgrounds will derive different conclusions.The result is that the new logic can not only maintain the rational requirement of the Stone representation theorem but can also make decisions more flexibly and effectively.The conclusion is that the generalized probabilistic logic can serve artificial intelligence more effectively.To meet the need of mechanistic artificial intelligence,this paper proposes the grammar-pragmatic docking method and the goal-driven backward reasoning.Finally,a mathematical proof is given for three couples of continuous operators in universal logic.

关 键 词：机制主义人工智能 泛逻辑 计量概率逻辑 因素空间 模糊集 可能性空间 谓词演算 随机集落影 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]