模糊模态集合论及其多元G值模型  

Fuzzy Modal Set Theory and Its Multi-G-valued Model

作　　者：杨帆 YANG Fan(College of Public Administration and Humanities,Dalian Maritime University,Dalian 116026,China)

机构地区：[1]大连海事大学公共管理与人文艺术学院,辽宁大连116026

出　　处：《模糊系统与数学》2024年第4期11-20,共10页Fuzzy Systems and Mathematics

基　　金：中央高校基本科研业务费专项资金资助“面向机器定理证明的模糊逻辑研究”(3132022308)。

摘　　要：为了构造基于模糊模态逻辑的ZF型集合论,从Godel模态逻辑的□片段出发构造其一阶形式G□∀△,给出其公理系统和模型,以此为底层逻辑构造ZF型模糊模态集合论GZF。结合集合论多元宇宙观的思想,提出了GZF的多元G值模型,并分析了构造模糊模态集合论的一些其他可能方案。In order to construct a ZF-style set theory based on fuzzy modal logic,the □-fragment of Godel modal logic is utilized to formulate its first-order variant G□∀△,for which the axiomatic system and model are presented.The ZF-style fuzzy modal set theory GZF is developed with G V as the underlying logic.Drawing upon the idea of multiverse view in set theory,a multi-G-valued model for GZF is proposed,and several alternative approaches for constructing fuzzy modal set theorys are analysed.

关 键 词：模糊模态集合论 Godel模态逻辑 模糊集合论 

分 类 号：O159[理学—数学]