A relational calculus with set operators, its safety, and equivalent graphical languages

The authors propose a relational calculus (RC/S) which uses set comparison and set manipulation operators to replace universal quantifiers and negations. It is argued that compared to the Codd relational calculus (RC), RC/S queries are easier to construct and comprehend. It is proved that the expressive power of RC is equivalent to the expressive power of RC/S, and algorithms for translating an RC query into an RC/S query and vice versa are given. A safe RC/S query is defined as one that has finite output and can be evaluated in finite time. Then a subset of RC/S queries, called RC/S* is defined, and it is proved that RC/S* is safe. RC/S* is compared to the existing largest safe subsets of RC, i.e. the evaluable formulas and the allowed formulas. Algorithms are given to transform any evaluable formula into an RC/S* query, and some RC/S* formulas that are not evaluable are given. RC/S* queries can be directly implemented using a graphical language similar to Query-by-Example (QBE). Two different graphical languages are described that are equivalent to the RC/S* in expressive power, and these languages are compared to QBE