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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.
In the first step, the relational algebra is extended with new algebraic operators to facilitate more expensive computationally processes of data mining tasks.
Let us define the extensional relational algebra for the FOL by
Similar to the relational algebra discussed in 5.1, primitive data types like integers and user-defined data types in programming languages are those whose syntactical algebras are seen as identical to the semantic algebras.
Persuaded that many applications will never reach the limitations of the widespread relational data model this article focuses on traditional relational algebra equipped with extra features that allow query relaxation and similarity searches.
Relational Algebra can be viewed as a data manipulation language for relational model.
More subtly, Chandra [1981] proposed the study of when and how for-each loops can be given a deterministic semantics, in the context of a programming language based on relational algebra and relational assignment, as an interesting research issue.
Does it mean that the relational algebra is in some sense inadequate as a basic relational query language?
Axioms (1)-(11) say that the structure is an idempotent semiring under +, [center dot], 0, and 1, and the remaining axioms (12)-(17) say essentially that * behaves like the Kleene star operator of formal language theory or the reflexive transitive closure operator of relational algebra. See Kozen [1994] for an introduction.
By redefining the basic operators of relational algebra in order to cope with the weights (and their probabilistic interpretation), the laws of relational algebra remain valid, and we get a probabilistic relational algebra (PRA).
Figure 1 shows the results of implementing the relational algebra operators (queries Q1 to Q5).
* We then define a theoretical annotated temporal algebra (TATA) in Section 5 and show how the classical relational algebra operations can be extended to the case of annotated tuples.

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