Generalized possibility computation tree logic with frequency and its model checking

In recent years, there has been significant research in the field of possibilistic temporal logic. However, existing works have not yet addressed the issue of frequency, which is a common form of uncertainty in the real world. This article aims to fill this gap by incorporating frequency information into possibilistic temporal logic and focusing on the model-checking problem of generalized possibility computation tree logic (GPoCTL) with frequency information. Specifically, we introduce generalized possibility computation tree logic with frequency (GPoCTL_F). Although its syntax can be considered as an extension of frequency constraints of the always operator (□) in GPoCTL, they are fundamentally different in semantics and model-checking methods. To facilitate this extension, useful frequency words such as “always”, “usually”, “often”, “sometimes”, “occasionally”, “rarely”, “hardly ever” and “never” are defined as fuzzy frequency operators in this article. Therefore, this article focuses on investigating the model-checking problem of the frequency-constrained always operator. In addition, we analyze the relationship between some GPoCTL_F path formulas and GPoCTL path formulas. Then, we provide a model-checking algorithm for GPoCTL_F and analyze its time complexity. Finally, an example of a social network is used to illustrate the calculation process of the proposed method and its potential applications.