Even more generic solution construction in Valuation-Based Systems
  Valuation algebras abstract a large number of formalisms for automated
reasoning and enable the definition of generic inference procedures. Many of
these formalisms provide some notions of solutions. Typical examples are
satisfying assignments in constraint systems, models in logics or solutions to
linear equation systems.
  Recently, formal requirements for the presence of solutions and a generic
algorithm for solution construction based on the results of a previously
executed inference scheme have been proposed in the literature. Unfortunately,
the formalization of Pouly and Kohlas relies on a theorem for which we provide
a counter example. In spite of that, the mainline of the theory described is
correct, although some of the necessary conditions to apply some of the
algorithms have to be revised. To fix the theory, we generalize some of their
definitions and provide correct sufficient conditions for the algorithms. As a
result, we get a more general and corrected version of the already existing
theory.
