Systems for Knowledge and Belief

We investigate modal systems for knowledge and belief, taking as a starting point a logic that was originally introduced by Kraus and Lehmann. We derive several properties and discuss (their) consequences for the epistemic operators. Kraus and Lehmann observed that adding the axiom B,(f —+ B,K,(p to the system gives a collapse of knowledge and belief: (Kitp +* Bi<p). We investigate the cause(s) of this problem and suggest a 'similar' system that does allow the same axiom without the mentioned collapse. We consider as the main benefit of this paper, however, the techniques that arc developed to come to this solution. It appears that applying basic correspondence theory to a multi-modal system allows a systematic examination of possible combinations of epistemic operators.