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

Studies in Logic, Vol. 17, No. 3 (2024): 86–101                  PII: 1674­3202(2024)­03­0086­16

Xiaoxuan Fu, Zhiguang Zhao

Abstract. 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.