Since the problem of logical omniscience was identified, several proposals have tried to model the knowledge of ‘real’ agents with limited reasoning abilities. One of the most important proposals, awareness logic, relies on the concept of awareness in order to distinguish what the agent ‘truly’ knows and what she could get out of it. Still, the notion of awareness can be interpreted in different ways: it can be understood as what the agent simply entertains, without having any attitude in favour or against (awareness of), but also as what she has consciously recognised as true (awareness that).
A previous proposal introduced a combination of these two possible interpretations at a conceptual level. This presentation proposes a formal framework (a semantic model and a language to describe it) that captures these two interpretations of the notion of awareness, as well as the epistemic notions that arise from their combination, such as implicit knowledge, explicit
knowledge or justification. The framework provides tools not only for understanding the notions’ subtle interaction, but also for representing some of the different epistemic actions (deductive inference, changes in awareness, external communication) that affect them.