模态计数逻辑ML(#)在不同框架类下的可判定性  

Decidability for Modal Logic with Counting ML(#)in Different Frame Classes

作　　者：付小轩 赵之光 Xiaoxuan Fu;Zhiguang Zhao(School of Humanities,China University of Political Science and Law;School of Mathematics and Statistics,Taishan University)

机构地区：[1]中国政法大学人文学院 [2]泰山学院数学与统计学院

出　　处：《逻辑学研究》2024年第3期86-101,共16页Studies in Logic

基　　金：supported by Tsinghua University Initiative Scientific Research Program;supported by Taishan Young Scholars Program of the Government of Shandong Province,China(No.tsqn201909151);Shandong Provincial Natural Science Foundation,China(No.ZR2023QF021);Support Plan on Science and Technology for Youth Innovation of Universities in Shandong Province(No.2021KJ086)。

摘　　要：在本文中,我们给出模态计数逻辑ML(#)在不同框架类下的可满足性的判定过程。我们使用两种方法,一种是通过修改ML(#)相对于全部克里普克框架的可满足性的判定算法,另一种是将ML(#)的可判定性归约到基本模态逻辑。我们还证明了分次模态计数逻辑GML(#)相对于全部克里普克框架的可判定性。In the present paper,we give the decision procedure of satisfiability of modal logic with counting ML(#)in different frame classes,by two types of methods,one by modifying the decision algorithm of satisfiability for ML(#)with respect to the class of all Kripke frames as described by J.van Benthem and T Icard(2021).the other by reducing decidability of ML(#)to that of basic modal logic.We also show the decidability of graded modal logic with counting GML(#)with respect to the class of all Kripke frames.

关 键 词：可满足性 模态逻辑 可判定性 归约 克里普克 判定算法 框架类 判定过程 

分 类 号：B815.1[哲学宗教—逻辑学]