D3-randomized truth degree of formulas in logic system Godel 3

Computer Engineering and Applications ›› 2011, Vol. 47 ›› Issue (5): 35-36.

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D3-randomized truth degree of formulas in logic system Godel 3

ZUO Weibing1，CHENG Weili1，MENG Yongsheng2

1.School of Mathematics and Information Science，North China Institute of Water Resources and Electric Power，Zhengzhou 450011，China
2.Mucheng Middle School of Wuzhi，Jiaozuo，Henan 454950，China

Received:1900-01-01 Revised:1900-01-01 Online:2011-02-11 Published:2011-02-11

逻辑系统G3中命题的D3-随机真度理论

左卫兵1，程伟丽1，孟永胜2

1.华北水利水电学院数学与信息科学学院，郑州 450011
2.武陟县木城初中，河南焦作 454950

Abstract

Abstract:

By means of randomization，the concept of D3-randomized truth degree of formulas in logic system Godel 3 is introduced；it is proved that the set of values of D3-randomized truth degree of formulas has no isolated point in [0，1].The concepts of D3-similarity degree and D3-pseudo-metric are also introduced；it is proved that there is no isolated point in D3-logic metric space.Three different types of approximate reasoning patterns are proposed in D3-logic metric space.The theories of consistency and independence of formulas are developed.

Key words: randomized vector sequence, D3-randomized truth degree, D3-similarity degree, approximate reasoning, independence

摘要： 通过引入随机向量序列对赋值集进行随机化，在逻辑系统G3中提出了公式的D3-随机真度的概念，证明了全体公式的D3-随机真度之集在[0，1]中没有孤立点；提出了D3-相似度和D3-伪距离，证明了在D3-逻辑度量空间中没有孤立点；在D3-逻辑度量空间中提出3种不同类型的近似推理模式；引入公式间的相容与独立的概念，研究了其关系。为进一步研究随机推理奠定了基础。

关键词: 随机向量序列, D3-随机真度, D3-相似度, 近似推理, 独立性

ZUO Weibing1，CHENG Weili1，MENG Yongsheng2. D3-randomized truth degree of formulas in logic system Godel 3[J]. Computer Engineering and Applications, 2011, 47(5): 35-36.

左卫兵1，程伟丽1，孟永胜2. 逻辑系统G3中命题的D3-随机真度理论[J]. 计算机工程与应用, 2011, 47(5): 35-36.

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D3-randomized truth degree of formulas in logic system Godel 3

逻辑系统G3中命题的D3-随机真度理论

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