扩展模态语言中模态可定义性的不可判定性结果  

Undecidability Results of Modal Definability in Extended Modal Languages

作　　者：赵之光 Zhiguang Zhao(School of Mathematics and Statistics,Taishan University)

机构地区：[1]泰山学院数学与统计学院

出　　处：《逻辑学研究》2021年第6期25-40,共16页Studies in Logic

基　　金：The research of the author is supported by Taishan University Starting Grant“Studies on Algebraic Sahlqvist Theory”and the Taishan Young Scholars Program of the Government of Shandong Province,China(No.tsqn201909151).

摘　　要：在本文中,我们使用Balbiani和Tinchev的稳定类方法证明在加全称模态词的模态语言L_(U)、时态语言L_(T)、混合语言L_(H),L_(H(@))中,Chagrova定理成立,即一阶公式相对于特定框架类的模态/时态/混合可定义性问题是不可判定的。In the present paper,we apply the methodology in Balbiani and Tinchev(2016)to show that for the modal language with universal modality L_(U),tense language L_(T),hybrid languages L_(H),L_(H(@)),Chagrova’s theorem holds that the modal/tense/hybrid definability of firstorder sentences with respect to certain classes of frames is undecidable,by using similar techniques as stable classes of Kripke frames.

关 键 词：可定义性 不可判定性 混合语言 模态词 LH 时态 

分 类 号：B815.1[哲学宗教—逻辑学]