计算机工程与应用 ›› 2011, Vol. 47 ›› Issue (5): 35-36.

• 研究、探讨 • 上一篇    下一篇

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. 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
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2011-02-11 发布日期:2011-02-11

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

ZUO Weibing1,CHENG Weili1,MENG Yongsheng2   

  1. 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

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

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