Epistemic logic and logical omniscience: A survey

Abstract

This survey brings together a collection of epistemic logics and discusses their approaches in alleviating the logical omniscience problem. Of particular note is the logic of implicit and explicit belief. Explicit belief refers to information actively held by an agent, while implicit belief refers to the logical consequence of explicit belief. Ramifications of Levesque's logic include nonstandard epistemic logic and the logics of awareness and local reasoning. Models of nonstandard epistemic logic are defined with respect to nonstandard proportional logic to weaken its semantics. In the logic of awareness, an agent can only believe a concept that it is aware of. Closely related to awareness are S-1 and S-3 epistemic operators which can be used to model skeptical and credulous agents. The logic of local reasoning provides a semantics for representing the fact that agents can have different clusters of beliefs which may contradict each other. Other variations include epistemic structures which are generalizations of the logic of local reasoning and fusion epistemic models which provide an account that agents can combine information conjunctively or disjunctively. Another closely related approach is the logic of explicit propostions which captures the insight that agents can hold beliefs independently without putting them together. © 1997 John Wiley & Sons, Inc.