A logical formalism for the subjective approach in a multi-agent setting

Representing an epistemic situation involving several agents depends very much on the modeling point of view one takes. In fact, the interpretation of a formalism relies quite a lot on the nature of this modeling point of view. Classically, in epistemic logic, the models built are supposed to represent the situation from an external and objective point of view. We call this modeling approach the objective approach. In this paper, we study the modeling point of view of a particular agent involved in the situation with other agents. We propose a logical formalism based on epistemic logic that this agent can use to represent `for herself' the surrounding world. We call this modeling approach the subjective approach. We then set some formal connections between the subjective approach and the objective approach. Finally we axiomatize our logical formalism and show that the resulting logic is decidable.