Paper Info
Title
On the logical implication of multivalued dependencies with null values
Abstract
The implication of multivalued dependencies (MVDs) in relational databases has originally been defined in the context of some fixed finite universe (Fagin 1977, Zaniolo 1976). While axiomatisability, implication problem and many design problems have been intensely studied with respect to this notion, almost no research has been devoted towards the alternative notion of implication in which the underlying universe of attributes is left undetermined (Biskup 1980).A milestone in the advancement of database systems was the permission of null values in databases. In particular, many achievements on MVDs have been extended to encompass incomplete information. Multivalued dependencies with null values (NMVDs) were defined and axiomatised in (Lien 1982). The definition of NMVDs is again based on a fixed underlying universe of attributes, and any complete set of inference rules requires therefore some version of the complementation rule.In this paper we show that the axiomatisation in (Lien 1982) does not reflect the fact that the complementation rule is merely a means to achieve database normalisation. Moreover, we provide an alternative axiomatisation for NMVDs that does reflect this property. We also suggest an alternative notion for the implication of NMVDs in which the underlying universe is left undetermined, and propose several sound and complete sets of inference rules for this notion. Moreover, a correspondence between (minimal) axiomatisations in fixed universes that do reflect the property of complementation and (minimal) axiomatisations in undetermined universes is shown.
Year
Venue
Keywords
2006
CATS
fixed universe,logical implication,implication,multivalued dependency,complete set,database theory,underlying universe,null values,complementation rule,fixed underlying universe,fixed finite universe,multivalued depen- dency,axiomatisation,null value,alternative notion,inference rule,relational database,incomplete information
Field
DocType
ISBN
Permission,Discrete mathematics,Logical consequence,Lien,Multivalued dependency,Relational database,Computer science,Database theory,Rule of inference,Complete information
Conference
1-920682-33-3
Citations 
PageRank 
References 
7
0.46
35
Authors
1
Name
Order
Citations
PageRank
Sebastian Link130719.17