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模态计数逻辑ML(#)在不同框架类下的可判定性

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

付小轩、赵之光

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中国政法大学人文学院

泰山学院数学与统计学院

Tsinghua University Initiative Scientific Research ProgramTaishan Young Scholars Program of the Government of Shandong Province,ChinaShandong Provincial Natural Science Foundation,ChinaSupport Plan on Science and Technology for Youth Innovation of Universities in Shandong Province

tsqn201909151ZR2023QF0212021KJ086

2024

逻辑学研究
中山大学 中国逻辑学会

逻辑学研究

CSSCICHSSCD
影响因子：0.464
ISSN：1674-3202
年,卷(期)：2024.17(3)
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