An abductive explanation of a problem "G" is a set of positive (and sometimes also negative) ground instances of the abducible predicates, such that, when these are added to the logic program P, the problem "G" and the integrity constraints IC both hold. Thus abductive explanations extend the logic program P by the addition of full or partial definitions of the abducible predicates. In this way, abductive explanations form solutions of the problem according to the description of the problem domain in P and IC. The extension or completion of the problem description given by the abductive explanations provides new information, hitherto not contained in the solution to the problem. Quality criteria to prefer one solution over another, often expressed via integrity constraints, can be applied to select specific abductive explanations of the problem "G".