Expressive power of linear-temporal logic based on generalized possibility measures

Model checking of linear-time properties based on possibility measures was developed by Li and Li (2013). However, the linear-time properties considered in the previous work were classical and qualitative, possibility information of the systems was not considered thoroughly at all. Therefore, the quantitative model checking of fuzzy linear-time properties based on generalized possibility measures was studied by Li (2016). This paper is a continuation of the above work. In this paper, we study the expressive power of possibilistic linear-temporal logic (PoLTL). Unlike possibilistic computation tree logic (PoCTL) in which the expressiveness of PoCTL is more powerful than computation tree logic (CTL), it is surprising that PoLTL is as expressive as linear-temporal logic (LTL). Furthermore, the comparison between PoLTL and generalized PoLTL (GPoLTL) is given. It is shown that the expressiveness of GPoLTL with restrained conditions is the same as PoLTL when semantics of GPoLTL is interpreted in the frame of possibilistic Kripke structure.