Modeling "and if possible" and "or at least": Different Forms of Bipolarity in Flexible Querying

This research note revisits an important issue with respect to the representation of preference queries, namely the modeling of “if possible” in requirements of the form “\(A\) and if possible \(B\)”. We mainly distinguish between two types of understanding: either (i) \(A\) and \(B\) are requirements of the same nature and are viewed as constraints with different levels of priority, or (ii) they are of different nature (only \(A\) induces constraint(s) and \(B\) is only used for breaking ties among items that are equally satisfying \(A\)). We indicate that the two views are related to different types of bipolarity, and discuss them in relation with possibilistic logic. The disjunctive dual of the first view (“\(A\) or at least \(B\)”) is then presented in this logical setting. We also briefly mention the idea of an extension of the second view where \(B\) may refer both to bonus conditions or malus conditions that may increase or decrease respectively the interest in an item satisfying \(A\).