Possibility semantics was originally proposed by Humberstone, and has received an increasing amount of attention in recent years, as an alternative modeling for classical and intuitionistic logics.
In this talk, we will consider the following problem: how we can generalize possibility semantics to logics of dynamical systems? For this, in the first part, we will review possibility semantics for propositional modal logic and intuitionistic propositional logic. Moreover, we will survey some of the results were obtained so far in this area.
In the second part, we will recall dynamic topological logic and some well-known facts about it. This multimodal logic was introduced by Kremer and Mints for reasoning about topological dynamics. Finally, we will present a logic of dynamical systems based on the possibility models. (Partly joint with Nick Bezhanishvili and Guillaume Massas, and with Morteza Moniri).