Knowledge updates: Semantics and complexity issues

We consider the problem of updating of an agent’s knowledge. We propose a formalmethod of knowledge update on the basis of the semantics of modal logic S5. Inour method, an update is specified according to the minimal change on both theagent’s actual world and knowledge. We discuss general minimal change propertiesof knowledge update and show that our knowledge update operator satisfies all theupdate postulates of Katsuno and Mendelzon. We characterize several specific formsof knowledge update which have important applications in reasoning about changeof agents’ knowledge. We also examine the persistence property of knowledge andignorance associated with knowledge update. We then investigate the computational complexity of model checking for knowledgeupdate. We first show that in general the model checking for knowledge update isΣ2 -complete. We then identify a subclass of knowledge update problems that haspolynomial time complexity for model checking. We point out that some importantknowledge update problems belong to this subclass. We further address another in-teresting subclass of knowledge update problems for which the complexity of modelchecking is NP-complete.