Intricate Axioms as Interaction Axioms

Abstract

In epistemic logic, some axioms dealing with the notion of knowledge are rather convoluted and difficult to interpret intuitively, even though some of them, such as the axioms.2 and.3, are considered to be key axioms by some epistemic logicians. 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 theory dealing with the characterization of axioms in terms of interaction axioms in modal logic. We then apply the main results and methods of this theory to obtain specific results related to epistemic and doxastic logics.