中介逻辑与中介公理集合论的综述

Survey of Medium Logics and Medium Axiom Set Theory

以中介逻辑演算系统和中介公理集合论为主要内容的中介数学系统是一种在数学基础意义上将精确性量性对象扩展到模糊量性对象的系统,它对数学的逻辑基础和集合论研究产生了重要影响。文中主要从下面3个方面论述:中介数学系统的研究背景;中介数学系统的基本内容及其与经典数学系统的关系,其中简要介绍了中介概念、中介原则、中介逻辑演算系统、中介公理集合论和中介数学系统的研究现状;有关中介逻辑的学术争论,特别围绕中介逻辑是不是一个新逻辑引用了正反双方的意见。此外,还展望了中介数学系统的应用前景。

Medium logic calculus systems （ML） and medium axiom set theory （MS） are main contents of medium mathematics systems（MMS） is a new system that extends precise quantity objects to fuzzy ones in terms of mathematical foundation. MMS has important influence on the research of logical foundation of mathematics and set theory. The contents of this paper include the research background of MMS, fundamentals of MMS and its relation with classical mathematics systems, brief introduction is given to medium concepts, medium principle, medium logic calculus systems, medium axiom set theory and the current situation of MMS research , as well as the academic disputation about ML, especially the argument on whether or not ML is a new logic. In addition, the application prospect of MMS is also provided.