An Equivalence Between Relational Database Dependencies and a Fragment of Propositional Logic

Abstract

It is known that there is an eqmvalence between functional dependencies m a relatmonal database and a certain fragment of proposmonal logic Thins eqmvalence is extended to include both functional and multivalued dependencmes. Thus, for each dependency there is a corresponding statement m proposmonal logic. It ms then shown that a dependency (funcuonal or multivalued) is a consequence of a set of dependencies ff and only ff the corresponding proposiuonal statement ~s a consequence of the corresponding set of proposmonal statements. Examples are given to show that these techniques are valuable mn provmdmg much shorter proofs of theorems about dependencies than have been obtained by more tradmonal means It is shown that this eqmvalence cannot be extended to include either join dependencies or embedded multmvalued dependencies.KEY WORDS AND PHRASES. relational database, functmonal dependency, multmvalued dependency, embedded multivalued dependency, join dependency, proposmUonal logmc CR CATEGORIES: 4.33, 5 21

On the Structure of Armstrong Relations for Functional Dependencies

“…In fact, Sagiv et al [21 ] show that if 2; is a set of dependencies (FDs or MVDs), if ~ is a single dependency, and if R is a relation that obeys 2; but not ~, then R has a two-tuple subrelation that obeys 2; but not ~ (a subrelation is a subset of the tuples). The proof is much harder than the proof of Lemma 3.1.…”

Monoidal functional dependencies

“…This is analogous to [17] (cf. also [13,42]) which shows that the logic of the classic FDs is in fact a particular propositional fragment. In this sense, the logic of MFDs we describe in the paper is a particular propositional fragment of Höhle's monoidal logic [29].…”

On a new class of Boolean dependencies

“…For th e equal m appings m entioned in E xam ple 2.1 several classes o f Boolean dependencies were investigated. Boolean dependencies were introduced in [11]. Positive B oolean dependencies are stu d ied in [3,4].…”

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