Abstract
AbstractBelief operators play an important role in epistemic analyses of games. For any event, a belief operator determines the set of states where this event is (in some precise sense) believed. Belief operators may satisfy different kinds of properties, like if one event implies another, then belief of the former implies belief of the latter (monotonicity) if two events are believed, then the conjunction is also believed an event that is always true is always believed an event that is never true is never believed if an event is believed, then the event that the event is believed is also believed (positive introspection), and if an event is not believed, then the event that the event is not believed is believed (negative introspection). Belief operators satisfying this list are called KD45 operators.1
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