A formal model for Explicit Knowledge as Awareness-of plus Awareness-that

In the context of the problem of logical omniscience, several frameworks have been proposed to model the knowledge of 'real' agents with limited reasoning abilities. One of the most important, awareness logic, relies on the concept of awareness for distinguishing what the agent 'truly' knows from what she could get if she were aware of all formulas. 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). This paper proposes a formal framework that captures these two interpretations of the notion of awareness, discussing the further epistemic notions that arise from their combination (e.g., implicit knowledge and explicit knowledge) while also studying their properties and the way they interact with one another.