**2. Preliminaries**

In this section, firstly, we introduce temporal logics including such as CDL∗ and its fragments LDL, LTL, and CTL∗. Then we introduce strategic logics whose underlying logics are LTL and CTL∗.

In this paper, we fix two non-empty finite sets, which are atomic proposition set *AP*, agent set *Ag*, and one nonempty countable set of strategy variable *Var*. By L(*AP*), we denote the set of propositional formulas over *AP*. In this paper, we use *true* (resp. *f alse*) to refer to valid (resp. contradiction) formula.
