A Fourth Normal Form for Possibilistic Data

Abstract

Relational database design addresses applications for data that is certain. Modern applications require the handling of uncertain data. Indeed, one dimension of big data is veracity. Ideally, the design of databases helps users quantify their trust in the data. For that purpose, we need to establish a design framework that handles responsibly any knowledge of an organization about the uncertainty in their data. Naturally, such knowledge helps us find database designs that process data more efficiently. In this paper, we apply possibility theory to introduce the class of possibilistic multivalued dependencies that are a significant source of data redundancy. Redundant data may occur with different degrees, derived from the different degrees of uncertainty in the data. We propose a family of fourth normal forms for uncertain data. We justify our proposal showing that its members characterize schemata that are free from any redundant data occurrences in any of their instances at the targeted level of uncertainty in the data. We show how to automatically transform any schema into one that satisfies our proposal, without loss of any information. Our results are founded on axiomatic and algorithmic solutions to the implication problem of possibilistic functional and multivalued dependencies which we also establish.