Possibilistic cardinality constraints and functional dependencies

Abstract

Cardinality constraints and functional dependencies together can express many semantic properties for applications in which data is certain. However, modern applications need to process large volumes of uncertain data. So far, cardinality constraints and functional dependencies have only been studied in isolation over uncertain data. We investigate the more challenging real-world case in which both types of constraints co-occur. While more expressive constraints could easily be defined, they would not enjoy the computational properties we show to hold for our combined class. Indeed, we characterize the associated implication problem axiomatically and algorithmically in linear input time. We also show how to summarize any given set of our constraints as an Armstrong instance. These instances help data analysts consolidate meaningful degrees of certainty by which our constraints hold in the underlying application domain.