Boolean Coherence: Does it make sense?

We continually face the problem of making sense of the world by resolving conflicting reports from multiple sources of information. This is particularly so if we attempt to formulate Qualitative Safety1 Arguments. Traditional logic offers little to assist in this process. In every day reasoning we usually assume that, without information to the contrary, we should use all information from all sources and that “information to the contrary” is the presence of an inconsistency between the sources. In order to resolve these conflicts we must make use of additional information which gives preference to one source of information over another when conflict arises between sources. The suggestion put forward in this note is that it is possible to reach a ‘best’ conclusion by taking the most coherent theory that respects the preference ordering on sources and that this theory is the maximal consistent theory with respect to the ordering. This process is parameterized by an underlying notion of logic that provides the notions of consistency and entailment. This notion is straightforward when applied to the standard notion of a strict preference ordering but is a little more involved when we consider partially ordered preferences.