Abstract. Handling inconsistency is an inherent part of decision making in traditional agri-food chains – due to the various concerns involved. In order to explain the source of inconsistency and represent the existing conflicts in the ontological knowledge base, argumentation theory can be used. However, the current state of art methodology does not allow to take into account the level of significance of the knowledge expressed by the various ontological knowledge sources. We propose to use preferences in order to model those differences between formulas and evaluate our proposal practically by implementing it within the INRA platform and showing a use case using this formalism in a bread making decision support system.