Justification for inclusion dependency normal form

Abstract

AbstractÐFunctional dependencies (FDs) and inclusion dependencies (INDs) are the most fundamental integrity constraints that arise in practice in relational databases. In this paper, we address the issue of normalization in the presence of FDs and INDs and, in particular, the semantic justification for Inclusion Dependency Normal Form (IDNF), a normal form which combines Boyce-Codd normal form with the restriction on the INDs that they be noncircular and key-based. We motivate and formalize three goals of database design in the presence of FDs and INDs: noninteraction between FDs and INDs, elimination of redundancy and update anomalies, and preservation of entity integrity. We show that, as for FDs, in the presence of INDs being free of redundancy is equivalent to being free of update anomalies. Then, for each of these properties, we derive equivalent syntactic conditions on the database design. Individually, each of these syntactic conditions is weaker than IDNF and the restriction that an FD not be embedded in the righthand side of an IND is common to three of the conditions. However, we also show that, for these three goals of database design to be satisfied simultaneously, IDNF is both a necessary and sufficient condition.Index TermsÐRelational database design, normal forms, functional dependency, inclusion dependency.

Mapping between Alloy Specifications and Database Implementations

“…For this to be viable, the resulting database schema should be free of insertion and update anomalies, which is quite difficult to guarantee when mixing INDs and FDs due to non-trivial interactions between both sets of dependencies. One possibility we are researching at the moment, is to restrict the database schemas to be in the socalled Inclusion Dependency Normal Form [9], a redundancyfree normal form where automatic integrity repair is feasible. The impact that this restriction has on the expressiveness of the source Alloy must be accessed carefully.…”

“…Ideally, we would like our notion of equivalence to ignore all redundant attributes, by converting first the schemas to the so called Attribute Redundancy Free Normal Form [9], but it is currently unknown how to do that in general. However, in this particular case, it suffices to eliminate redundant unary relations, using the following procedure: Definition V.8.…”

“…Clearly, the single attributes of both A and B are redundant, in the following sense [9]: Definition V.7. Given a database schema R, Σ i , Σ F , the i-th attribute of a relation schema R ∈ R is redundant if, whenever d is a database over R which satisfies Σ, then, for every tuple t ∈ r, if t[i] is replaced by a value v = t[i] then the resulting database does not satisfy Σ.…”

Analysis of Typed Inclusion Dependencies with Null Values

“…Продолжением проблемы взаимодействия зависимостей является построение со-ответствующих нормальных форм (IDNF), основанных на нормальной форме Бойса-Кодда и с ограничением в виде зависимостей включения для ациклических схем БД [7,8]. Впервые условия ацикличности схем БД были исследованы в [9].…”

“…Струк-турная интерпретация зависимостей включения в виде графа представлена в [10]. Хотя исследуются отличные от [8] условия ацикличности, в работе [11] показана связь между ними.…”