In the first step, the
relational algebra is extended with new operators that execute the most expensive processes of association and classification tasks.
Pirotte, "A precise definition of basic relational notions and of the
relational algebra," ACM SIGMOD Record, vol.13, no.1, pp.30-45, 1982.
* Rules for combining operands and operators to
relational algebra expression
In this section we consider a more specific framework of update methods implemented in the
relational algebra, inspired by the algebraic model of object-oriented database access introduced by Hull and Su [1989].
Since the
relational algebra and calculus are equivalent to pure first-order logic, they have [AC.sup.0] data complexity, cf.
So any expression in our probabilistic
relational algebra yields a probabilistic relation.
Compaction is the TP analog of duplicate elimination in the
relational algebra.
The estimate operator is classified by the
relational algebra operator (select, project, join), the property to be estimated (cardinality, distribution of values, and other parameters), and the underlying method (parametric, nonparametric, and ad-hoc).
This mapping assumes a mapping of SQL-92 to
relational algebra and defines temporal statements in terms of their mapping to well-defined temporal and conventional
relational algebra expressions.
Extending
Relational Algebra and Relational Calculus with
OQL queries in our framework are translated into a calculus format that serves as an intermediate form, and then are translated into a version of the nested
relational algebra. We use both a calculus and an algebra as intermediate forms because the calculus closely resembles current OODB languages and is easy to put into canonical form, while the algebra is lower-level and can be directly translated into the execution algorithms supported by database systems.
MATCH is a new operator for
relational algebra which provides a natural and nonprocedural means to express retrievals based on very complex patterns which are themselves stored as data.