[1]WANG Peizhuang,ZHOU Hongjun,HE Huacan,et al.Factorial information space and generalized probability logic[J].CAAI Transactions on Intelligent Systems,2019,14(5):843-852.[doi:10.11992/tis.201810021]
Copy

Factorial information space and generalized probability logic

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 14 Number of periods: 2019 5 Page number: 843-852 Column: 综述 Public date: 2019-09-05
Title:
Factorial information space and generalized probability logic
Author(s):
WANG Peizhuang1;  ZHOU Hongjun2;  HE Huacan3;  ZHONG Yixin4
1. Institute of Intelligence Engineering and Math, Liaoning Technical University, Fuxin 123000, China;
2. College of Mathematics, Shannxi Normal University, Xi’an 710062, China;
3. School of Computer Science, Northwestern Polytechnical University, Xi’an 710072, China;
4. Center for Intelligent Science and Technology, Beijing University of Posts Telecommunications, Beijing 100876, China
Keywords:
mechanism based artificial intelligence; universal logic; econometric probability logic; factors space; fuzzy sets; possibility space; predicate calculus; random falling shadow
CLC:
TP18
DOI:
10.11992/tis.201810021
Abstract:
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.
References:
[1] 钟义信. 高等人工智能原理:观念·方法·模型·理论[M]. 北京:科学出版社, 2014.
[2] 何华灿. 泛逻辑学原理[M]. 北京:科学出版社, 2001.
[3] LUKASIEWIEZ L. On three-valued logic[J]. Ruch filozifaczny, 1920, 5:170-171
[4] ZADEH L A. Fuzzy sets[J]. Information and control, 1965, 8(3):338-353.
[5] 王国俊. 计量逻辑学(I)[J]. 工程数学学报, 2006, 23(2):191-215 WANG Guojun. Quantitative logic (I)[J]. Chinese journal of engineering mathematics, 2006, 23(2):191-215
[6] SCHWEIZER B, SKLAR A. Probabilistic metric spaces[M]. New York:North Holland, 1983.
[7] 周红军. 概率计量逻辑及其应用[M]. 北京:科学出版社, 2015.
[8] 王国俊. 一类一阶逻辑公式中的公理化真度理论及其应用[J]. 中国科学:信息科学, 2012, 42(5):648-662 WANG Guojun. Axiomatic theory of truth degree for a class of first-order formulas and its application[J]. China science information, 2012, 42(5):648-662
[9] 裴道武. 基于三角模的模糊逻辑理论及其应用[M]. 北京:科学出版社, 2013.
[10] 张小红. 模糊逻辑及其代数分析[M]. 北京:科学出版社, 2008.
[11] 张小红, 折延宏. 模糊量词及其积分语义[M]. 北京:科学出版社, 2017.
[12] XU Yang, QIN Keyun, RUAN Da, et al. Lattice-valued logic:an alternative approach to treat fuzziness and incomparability[M]. Berlin, Heidelberg:Springer, 2003.
[13] ZADEH L A. Fuzzy sets as a basis for a theory of possibility[J]. Fuzzy sets and systems, 1978, 1(1):3-28.
[14] 汪培庄, SUGENO M. 因素场与模糊集的背景结构[J]. 模糊数学, 1982(2):45-54 WANG Peizhuang, SUGENO M. The factors field and background structure for fuzzy set[J]. Fuzzy mathematics, 1982(2):45-54
[15] 汪培庄. 模糊集与随机集落影[M]. 北京:北京师范大学出版社, 1985.
[16] STONE M H. The theory of representation for Boolean algebras[J]. Transactions of the American mathematical society, 1936, 40(1):37-111.
[17] DAVEY B A, PRIESTLEY H A. Introduction to lattices and order[M]. Cambridge:Cambridge University Press, 1990.
[18] 崔铁军, 汪培庄, 马云东. 01型空间故障树的结构化表示方法[J]. 大连交通大学学报, 2016, 37(1):82-87 CUE Tiejun, WANG Peizhuang, MA Yundong. Structured representation methods for 01 space fault tree[J]. Journal of Dalian Jiaotong University, 2016, 37(1):82-87
[19] 汪培庄. 因素空间理论:机制主义人工智能理论的数学基础[J]. 智能系统学报, 2018, 13(1):37-54 WANG Peizhuang. Factor space-mathematical basis of mechanism based artificial intelligence theory[J]. CAAI transactions on intelligent systems, 2018, 13(1):37-54
[20] 汪培庄. 模糊数学与优化[M]. 北京:北京师范大学出版社, 2013.
Similar References:

Memo

-

Last Update: 1900-01-01

Copyright © CAAI Transactions on Intelligent Systems