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In this paper we address the role of divergence and convergence in creative processes, and argue about the need to consider them in Computational Creativity research in the Genetic or Evolutionary Programming paradigm, being one's goal the problem of the Halt Condition in Genetic Programming. Here the candidate solutions are seen as evolutionary logic programs or theories, being the test whether a solution is optimal based on a measure of the quality-of-information carried out by those logical theories or programs. Furthermore, we present Conceptual Blending Theory as being a promising framework for implementing convergence methods within creativity programs, in terms of the logic programming framework.