定性推理经典方法的数学结构分析
首发时间:2005-04-28
摘要:在简单回顾了定性推理的目标和特征的基础上,从代数结构、信息复杂性等方面分析了现存的6个代表性定性推理理论。从代数结构上看,它们或大约在环的水平,或大约接近于域。从复杂性看,有的以一阶逻辑为演算核心,有的大约以实数域作为核心。从求解效率看,最坏情况大都倾向于到指数界,平均情况时好时坏,常在多项式界。最后,提出“一般的几何曲线”层次的演算体系是定性推理的最高数学抽象。
For information in English, please click here
Mathematical Structure Analysis of Classical Theories in Qualitative Reasoning
Abstract:Based on the brief review to the goals and characteristics of the existing qualitative reasoning, the 6 typical qualitative reasoning methods are analyzed from the algebraic structure, information complexity. They are of about or above rings, or near to fields in algebra, use the first order logic or simplified real number field in complexity, usually in polynomial times in the average case, and go to exponential times in the worst case in solution. Finally it is concluded that the highest mathematical abstraction of qualitative reasoning are f-mathematics, in which “the general curves” are the primal elements.
Keywords: Qualitative reasoning Mathematical structure Complexity Ring Field Artificial Intelligence
基金:
论文图表:
引用
No.1953168601114650****
同行评议
共计0人参与
勘误表
定性推理经典方法的数学结构分析
评论
全部评论0/1000