Counter-free keys and functional dependencies in higher-order datamodels

  • Authors:

  • Attila Sali;Klaus-Dieter Schewe

  • Affiliations:

  • Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary;Massey University, Information Science Research Centre, Palmerston North, New Zealand

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 2005

Quantified Score

Hi-index 0.00

Visualization

Abstract

We investigate functional dependencies (FDs) in the presence of several constructors for complex values. These constructors are the tuple constructor, list-, set-and multiset-constructors, an optionality constructor, and a disjoint union constructor. The disjoint union constructor implies restructuring rules, which complicate the theory. In particular, they do not permit a straightforward axiomatisation of the class of all FDs without a detour via weak functional dependencies (wFDs), i.e. disjunctions of functional dependencies, and even the axiomatisation of wFDs is not yet completely solved.Therefore, we look at the restricted class of counter-free functional dependencies (cfFDs). That is, we ignore subattributes that only refer to counting the number of elements in sets or multisets or distinguish only between empty or non-empty sets. We present a finite axiomatisation for the class of cfFDs.Furthermore, we study keys ignoring again the counting subattributes. We show that such keys are equivalent with certain ideals called HL-ideals. Based on that we introduce an ordering between key sets, and investigate systems of minimal keys. We give a sufficient condition for a Sperner family of HL-ideals being a system of minimal keys, and determine lower and upper bounds for the size of the smallest Armstrong-instance.