The purpose of this paper is to provide a formal model of a persuasion process in which a persuader tries to influence audience's beliefs. We focus on various interactions amongst agents rather than only exchange of arguments by verbal means. Moreover, in our approach the impact of the parties of the dispute on the final result of the persuasion is emphasized. Next, we present how to formalize this model using the modal system inspired by Logic of Graded Modalities and Algorithmic and Dynamic Logics. We also show how to investigate local and global properties of multi-agent systems which can be expressed in the language of the proposed logic.