Three structures for belief revision: plausability relations on states, relations of epistemic entrenchment on propositions and systems of spheres (hypertheories), are generalised to the non-linear (non-connected) case. The further generalisation to the case of sets of such structures is also investigated. A formal language with dynamic and doxastic (belief) modal operators (DDL) is used to establish interdefinability properties between the structures and complete axiomatisations are given.

The problem of iterated belief revision on non-linear structures is considered. The ideas and results of Darwiche & Pearl (1997) for iterated belief revision on linear structures are generalised to the non-linear case and axiomatisations in DDL are given.

The structures and results are used to investigate a particular application: the problem when there are multiple, possibly unreliable and possibly contradictory sources of information. A trustworthiness relation on sources of information together with the information supplied by the sources is used to generate a non-linear plausibility relation on states and forms the basis for a decision procedure about what to believe. A DDL-style language with multiple non-prioritised revision operators is used to investigate the resulting structures and complete axiomatisations are given.