Strict and tolerant antidivision queries with ordinal layered preferences

In this paper, we are interested in taking preferences into account for a family of queries inspired by the antidivision. An antidivision query aims at retrieving the elements associated with none of the elements of a specified set of values. We suggest the introduction of preferences inside such queries with the following specificities: (i) the user gives his/her preferences in an ordinal way and (ii) the preferences apply to the divisor which is defined as a hierarchy of sets. Different uses of the hierarchy are investigated, which leads to queries conveying different semantics and the property of the result delivered is characterized. Furthermore, the case where a conjunctive stratified antidivision query returns an empty set of answers is dealt with, and an approach aimed at relaxing such queries is proposed.