Prioritized Preferences and Choice Constraints

Abstract

It is increasingly recognised that user preferences should be addressed in many advanced database applications, such as adaptive searching in databases. However, the fundamental issue of how preferences impact the semantics and rankings in a relation is not resolved. In this paper, we model a user preference term involving one attribute as a hierarchy of its underlying data values and formalise the notion of Prioritized Preferences (PPs). We then consider multiple user preferences in ranking tuples in a relational table. We examine the impact of a given set of PPs on possible choices in ranking a database relation and develop a new notion of Choice Constraints (CCs) in a relation, r. Given two PPs, X and Y, a CC, X ≤ Y, is satisfied in r, if the choice of rankings according to Y is no less than that of X. Our main results are related to these two notions of PPs and CCs and their interesting interactions with the well-known Functional Dependencies (FDs). First, we exhibit a sound and complete set of three inference rules for PPs and further prove that for each closed set of PPs, there exists a ranking that precisely satisfies these preferences. Second, we establish a sound and complete set of five inference rules for CCs. Finally, we show the soundness and completeness of two mixed systems of FD-PPs and FD-CCs. All these results are novel and fundamental to incorporating user preferences in database design and modelling, since PPs, CCs and FDs together capture rich semantics of preferences in databases.