Peeva and Kyosev  developed a library for fuzzy relational calculus
over the fuzzy algebra([0,l], max, min).
However, the suggested time allocation shows the theory based approach emphasizes more on learning the concepts like relational algebra, relational calculus
, query processing and optimization, whereas the all-encompassing approach allocates lesser time and emphasis on these theoretical topics.
The legends of Figure 1 will be used in the representation of the relational calculus
of each one of the problems in the three classes.
Actually, once problems in these fields are formalized in terms of relational calculus
, these problems can be considered by using formulae of relations; that is, we need only calculus of relations in order to solve the problems.
Relational Algebra (RA) and Relational Calculus
(RC) are core components of relational theory.
The topics include using knowledge management as a tool to improve decision making processes, a knowledge-based code clone approach in embedded and real-time systems, using knowledge management and aggregation techniques to improve web effort estimation, an empirical study of requirement engineering practices in the Pakistani software industry, managing knowledge in open source software test processes, a software system for grading diabetic retinopathy by analyzing retinal images, and demonic fuzzy relational calculus
He includes exercises, a review of relational calculus
, and annotated suggestions for further reading (including Date's An Introduction to Database Systems, 2004).
Experience shows that students can infer the rigorous logic, such as the tuple relational calculus
, from natural language queries, but find it cumbersome to translate it to SQL.
In the relational model, Codd ([Cood,70]) developed the Relational Algebra (AR) and the Relational Calculus
(CR) as formal query languages, and he proved that the two languages are equivalent in their expressive power, and, further, equivalent to FO.
In a way, monoid comprehension resembles the tuple relational calculus
, but here query variables may range over multiple collection types, while the output of the comprehension may be of yet another collection type.
As a by-product, we obtain an elementary proof of the fact that parity test is not definable in the relational calculus
with polynomial inequality constraints.
Completeness would rule out automation, since specification languages are invariably more expressive than the relational calculus
, which is known to be undecidable [Schoenfeld 1979].