Among those who work in epistemic logic, the logic of knowledge
is usually identified with some rather strong modal logic, such as S4 or S5. At the same time,
many philosophers voice their dissatisfaction with the fact that normal modal logic contains
principles like the Kripke schema ("if you know that j and if you know that (if j then y), then
you know that y") and necessitation ("you know that all logical truths") -- principles that
certainly don't hold for actual knowledge.
In this talk I will say something about the relationship between actual and merely implicit knowledge, and also about how I would go about trying to construct a logic of actual knowledge.