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The modeling of epitesmic knowledge is a necessity of most systems dealing with some sort of artificial reasoning. There are several formalisms able to mathematically model someone's degrees of belief. A very popular one is the Bayesian theory, which is based on a prior knowledge of a probability distribution. Another model is the theory of evidence, or Dempster-Shafer theory, which provides a method for combining evidences from different sources without prior knowledge of their distributions. In this latter method, it is possible to assign probability values to sets possibilities rather than to single events only, and it is not needed to divide all the probability values among the events, once the remaining probability should be assigned to the environment and not to the remaining events, thus modeling more naturally certain classes of problems. There are some pitfalls however, in particular, the Dempster-Shafer theory does not model well evidences with a high degree of conflict, and evidences with the more probable possibility disjoint but with a less probable possibility in common tend to bias the results toward the less probable hypothesis in an illogical way, assigning 100% probability of it. In this paper, we present an extension of Dempster-Shafer theory that overcome the aforementioned pitfalls, allowing the combination of evidences with higher degrees of conflict, and avoiding the excessive tendency toward the common possibility of otherwise disjoint hypothesis. This is accomplished by means of a new rule of evidences combination that embodies the conflict among the evidences, modeling naturally the epitesmic reasoning.