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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (5): 67-73.doi: 10.6040/j.issn.1671-9352.0.2023.502

• • 上一篇    

一阶逻辑中的近似推理与强近似推理Symbol`@@

袁一丹,惠小静Symbolj@@,王前   

  1. 延安大学数学与计算机科学学院, 陕西 延安 716000
  • 发布日期:2025-05-19
  • 通讯作者: 惠小静(1973— ),女,教授,研究生导师,博士,研究方向为数理逻辑与不确定性推理. E-mail:xhmxiaojing@163.com
  • 作者简介:袁一丹(2000— ),女,硕士研究生,研究方向为数理逻辑与不确定性推理. E-mail:1757628434@qq.com*通信作者:惠小静(1973— ),女,教授,研究生导师,博士,研究方向为数理逻辑与不确定性推理. E-mail:xhmxiaojing@163.com
  • 基金资助:
    国家自然科学基金资助项目(12261090)

Approximate reasoning and strong approximate reasoning in first-order logic

YUAN Yidan, HUI XiaojingSymbolj@@, WANG Qian   

  1. School of Mathematics and Computer Science, Yanan University, Yanan 716000, Shaanxi, China
  • Published:2025-05-19

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摘要： 利用伪距离定义一阶逻辑度量空间中3种不同近似推理模式,证明不同近似推理模式之间的等价性,给出一种基于相似度的近似推理模式Γδα,研究该推理模式与3种不同近似推理模式之间的关系,最后提出强近似推理模式。

关键词: 一阶逻辑, 公理化真度, 近似推理, 强近似推理

Abstract: In the first-order logical metric space, three different types of approximate reasoning patterns are defined based on pseudo distance, and the equivalence relationship between the three approximate reasoning patterns is proved. In addition, a new approximate reasoning mode Γδα is proposed based on similarity, and the relationship between this reasoning mode and three reasoning modes is studied. Finally, a strong approximate reasoning mode is proposed.

Key words: first-order logic, axiomatic truth degree, approximate reasoning, strong approximate reasoning

中图分类号: 

  • O159
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