On the Complexity of Finding Second-Best Abductive Explanations
  While looking for abductive explanations of a given set of manifestations, an ordering between possible solutions is often assumed. The complexity of finding/verifying optimal solutions is already known. In this paper we consider the computational complexity of finding second-best solutions. We consider different orderings, and consider also different possible definitions of what a second-best solution is. 
Paolo Liberatore and Marco Schaerf
cs.LO cs.AI