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Merging beliefs depends on the relative reliability of their sources. When this is information is absent, assuming equal reliability is unwarranted. The solution proposed in this article is that every reliability profile is possible, and only what holds according to all of them is accepted. Alternatively, one source is completely reliable, but which one is not specified. These two cases motivate two existing forms of merging: maxcons-based merging and disjunctive merging.

A common assumption in belief revision is that the reliability of the information sources is either given, derived from temporal information, or the same for all. This article does not describe a new semantics for integration but studies the problem of obtaining the reliability of the sources given the result of a previous merging. As an example, corrections performed manually on the result of merging some databases may indicate that the relative reliability of their sources is different from what was previously assumed, helping subsequent data mergings.

When looking for a propositional abductive explanation of a given set of manifestations, an ordering between possible solutions is often assumed. While the complexity of computing optimal solutions is already known, in this paper we consider second-best solutions with respect to different orderings, and different definitions of what a second-best solution is: an optimal solution not already found, or a solution that is optimal among the ones not previously found.