axiom B is a theorem in S5 (viz. ), which says that what an agent does not know that they do not know is true: . The modal axiom B is true on any symmetric frame, but is very counterintuitive in epistemic logic: How can the ignorance on one's own ignorance imply truth? It is therefore debatable whether S4 describes epistemic logic better, rather than S5. Epistemic logic also deals with belief, not just knowledge. The basic modal operator is usually written B instead of K. In this case, though, the knowledge axiom no longer seems right—agents only sometimes believe the truth—so it is usually replaced with the Consistency Axiom, traditionally called D: which states that the agent does not believe a contradiction, or that which is false. When D replaces T in S5, the resulting system is known as KD45. This results in different properties for as well. For example, in a system where an agent "believes" something to be true, but it is not actually true, the accessibility relation would be non-reflexive. The logic of belief is called doxastic logic. Multi-agent systems When there are multiple agents in the domain of discourse where each agent i corresponds to a separate epistemic modal operator , in addition to the axiom schemata for each individual agent listed above to describe the rationality of each agent, it is usually also assumed that the rationality of each agent is common knowledge. Problems with the possible world model and modal model of knowledge If we take the possible worlds approach to knowledge, it follows that our epistemic agent a knows all the logical consequences of their beliefs (known as logical omniscience). If is a logical consequence of , then there is no possible world where is true but is not. So if a knows that is true, it follows that all of the logical consequences of are true of all of the possible worlds compatible with as beliefs. Therefore, a knows . It is not epistemically possible for a that not- given his knowledge that . This consideration was a part of what led Robert Stalnaker to develop two-dimensionalism, which can arguably explain how we might not know all the logical consequences of our beliefs even if there are no worlds where the propositions we know come out true but their consequences false. Even when we ignore possible world semantics and stick to