Queries mixing positive and negative associations and their weakening

This paper deals with queries involving two components: one describing desired associations, another specifying forbidden associations. In addition, those preferences are cited in the context of a hierarchy expressing some strength about what is wanted and rejected. So doing an ordinal ordering over the answers is made available in order to distinguish among the elements of the answer. The situation where no answer is returned is also tackled and it is proposed to soften the initial query in order to get a non-empty answer. It is shown that this can be achieved still using an ordinal framework which is an extension of the initial one.