破坏模态逻辑的算法对应理论  

Algorithmic Correspondence Theory for Sabotage Modal Logic

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》2022年第6期66-92,共27页Studies in Logic

基　　金：supported by Taishan University Starting Grant “Studies on Algebraic Sahlqvist Theory”;the Taishan Young Scholars Program of the Government of Shandong Province,China (tsqn201909151);the Support Plan on Science and Technology for Youth Innovation of Uni-versities in Shandong Province (2021KJ086)。

摘　　要：破坏模态逻辑是一种动态逻辑。它在静态模态逻辑的基础上加入了一个动态算子,解释成“在删掉一条边后,公式为真”。在本文中,我们试图解决一个开放问题,即给出破坏模态逻辑的Sahlqvist对应定理。我们定义破坏模态逻辑的Sahlqvist公式,并给出一个算法ALBASML来计算破坏模态逻辑的Sahlqvist公式的一阶对应。Sabotage modal logic(SML) is a kind of dynamic logic. It extends static modal logic with a dynamic modality which is interpreted as “after deleting an arrow in the frame,the formula is true”. In the present paper, we are aiming at solving an open problem stated in Aucher, van Benthem and Grossi(2018), namely giving a Sahlqvist-type correspondence the-orem(Sahlqvist 1975) for sabotage modal logic. In this paper, we define sabotage Sahlqvist formulas and give an algorithm ALBASMLto compute the first-order correspondents of sabo-tage Sahlqvist formulas. We give some remarks and future directions at the end of the paper.

关 键 词：模态逻辑 动态逻辑 对应定理 

分 类 号：B815.1[哲学宗教—逻辑学]