Axioms .2 and .4 as Interaction Axioms

ABSTRACT. In epistemic logic, some axioms dealing with the notion of knowledge are rather convoluted and it is difficult to give them an intuitive interpretation, even if some of them, like axioms .2 and .3, are considered by some epistemic logicians to be key axioms. We show that they can be characterized in terms of understandable interaction axioms relating knowledge and belief or knowledge and conditional belief. In order to show it, we first sketch a primitive theory dealing with the characterization of axioms in terms of interaction axioms in modal logic. We then apply its general results to obtain some specific results related to epistemic and doxastic logics.