基于真值的SBL_～公理化扩张系统的计量化  

Quantified axiomatic extension systems of SBL_～ based on truth value

作　　者：惠小静[1] 

机构地区：[1]延安大学数学与计算机科学学院,延安716000

出　　处：《中国科学：信息科学》2014年第7期900-911,共12页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:10771129);陕西省高水平大学建设专项资金(批准号:2012SXTS07)资助项目

摘　　要：本文首先在带有对合否定的△模糊逻辑系统SBL～中,运用△演绎定理和真值分布,论证了SBL～系统中有效推理的真值关系定理.其次以SBL～系统的公理化扩张Godel～为例,提出了△相似度、△距离,运用真值关系定理论证了△度量空间逻辑算子→,～的连续性,给出了公式与理论间距离的计算方法,从而实现了△模糊逻辑系统的计量化.最后在Godel～系统中提出了3种近似推理模式,并讨论了3种模式之间的关系.Based on △ deduction theorem and true value distribution, this paper proves true value relationship theorem of valid inference in A fuzzy logic system SBL- with involutive negation. Secondly, as an example of axiomatic extensions of SBL- system, Godel- is quantified by introducing △ similarity and △ distance. Then the paper proves the continuity of logic operators →,～ by using the true value relationship theorem, gives the method to calculate the distance between the formula and theory. Finally, this paper proposes three different types of approximate reasoning patterns and discusses the relationships between three modes in Godel-.

关 键 词：模糊逻辑 计量逻辑 概率逻辑 有效推理 真值 度量空间 

分 类 号：O141[理学—数学] O159[理学—基础数学]