Abstract
There is an established equivalence between relational database Functional Dependencies (FDs) and a fragment of switching algebra that is built typically of Horn clauses. This equivalence pertains to both concepts and procedures of the FD relational database domain and the switching algebraic domain. This study is an exposition of the use of switching-algebraic tools in solving problems typically encountered in the analysis and design of relational databases. The switching-algebraic tools utilized include purely-algebraic techniques, purely-visual techniques employing the Karnaugh map and intermediary techniques employing the variable-entered Karnaugh map. The problems handled include; (a) the derivation of the closure of a Dependency Set (DS), (b) the derivation of the closure of a set of attributes, (c) the determination of all candidate keys and (d) the derivation of irredundant dependency sets equivalent to a given DS and consequently the determination of the minimal cover of such a set. A relatively large example illustrates the switching-algebraic approach and demonstrates its pedagogical and computational merits over the traditional approach.
Highlights
It has been known for decades that there is an equivalence between relational database Functional Dependencies (FDs) and a fragment of propositional logic (Delobel and Casey, 1973; Fagin, 1977; Sagiv et al, 1981; Fagin, 1982; Russomano and Bonnell, 1999; Zhang, 2009a; 2009b; 2010; YiShun and ChunHua 2012)
Starting with a set of functional dependencies Ai → Ci,1≤i≤n, that constitutes a set S, we view these dependencies as propositional implications that we denote by the same symbols (Ai→ Ci, 1≤ i ≤), taking liberty to allow a little abuse of notation
The traditional database approach, adopted by almost all textbooks on database design is based on the heuristic application of axioms and lemmas for the manipulation of functional dependencies
Summary
It has been known for decades that there is an equivalence between relational database Functional Dependencies (FDs) and a fragment of propositional logic (Delobel and Casey, 1973; Fagin, 1977; Sagiv et al, 1981; Fagin, 1982; Russomano and Bonnell, 1999; Zhang, 2009a; 2009b; 2010; YiShun and ChunHua 2012). That fragment covers what is known as Horn clauses in switching theory (twovalued Boolean algebra). We demonstrate that such analysis and design can be facilitated, made more efficient, rendered algorithmic in nature, extended to problems of larger sizes and equipped with insightful visualization through the utilization of well established and readily-available tools of switching algebra
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