On Dealing with False Beliefs and Maintaining KD45n Property

Motivated by counterintuitive results of the update of a Kripke structure using an update model, such as the inability to correct false beliefs of agents or the creation of incoherent state of beliefs of agents, this paper explores a novel methodology for updating a Kripke structure using an update model. The paper shows that the new definition helps agents correct their false beliefs when they are full observers of a sensing action or a truthful announcement. Furthermore, the paper presents a sufficient condition for update models that guarantees that the resulting Kripke structure maintains the KD45 n property of the original Kripke structure if the update model is also KD45 n. In particular, the majority of update models recently described in the literature for reasoning about knowledge and beliefs of agents in multi-agent domains satisfy such sufficient condition. This implies that the KD45 n property will be maintained after the execution of an action sequence if the initial Kripke structure is KD45 n. These results can help guide the design of update models for compound actions in applications dealing with knowledge and beliefs; they can also be used by epistemic planners that employ update models to correct agents' false beliefs.