Database Reference
In-Depth Information
free relational view updates? Why is it not possible to always have such side-
effect free updates and which are the criteria to adopt in order to overcome such
problems? How can we use the concepts of the transitions obtained from the
RA
arrows in the Application plan of the categorial RDB machines
M
RC
(defined
in the previous chapter) for a formalization of the deletion (and insertion) by
minimal side-effects?
3. Why do we obtain a backward chaining propagation (w.r.t. the schema mapping
arrows) in the case of deletion and why do we obtain a forward chaining prop-
agation in the case of insertion? In the presence of cyclic graphs of the schema
mapping systems, infinite propagations are possible. For which kind of propa-
gation does this happen? Can we use the methods of the fixpoint operators used
in Sect.
4.2.4
in order to interrupt the infinite propagation (which generates the
infinite extensions of the relations in the database) and useless insertion of the
Skolem constants in our algebraic framework? (Why is it not possible in the
pure logic framework?)
4. The problem of the infinite propagations, in cyclic database mapping systems
with incomplete information, in Big Data Integration has a significant prob-
ability to happen. The logic used to specify the mappings based on SOtgds
(for incomplete information) in order to be well defined needs the models of
such logic theories, so that it will necessarily require the infinite processes
and hence it will be inapplicable in practice. Explain the difference from the
strong and weak Data Integration which is possible in the algebraic framework
based on the
DB
category. What is an epistemic point of view in the more
flexible weak integration? In which way can it be used for the P2P Data inte-
grations?
5. The denotational (non-abstract) DB-grammar for the database-mapping pre-
cesses in Definition
52
is coherent with the observational operational seman-
tics? Why? The database-mapping programs are well defined terms of the
abstract
GSOS
DB
signature
Σ
P
for a database-mapping processes presented
in Sect.
7.1
. Do this exercise: define an initial semantics for the denotational
(non-abstract) DB grammar and its algebra, based on the syntax algebra of the
GSOS
DB
signature
Σ
P
. Demonstrate that this initial semantics corresponds to
the isomorphism in Definition
53
.
6. The generation of the Labeled Transition Tree (LTS) of the database (process)
updates is based on the atomic transitions (insertion or deletion of the tuples).
How is such an atomic transition represented in the
DB
category? Why is it
useful to represent such a process tree by an (also infinite) set of equations,
and what are the variables of these equations? Why do we obtain a guarded
system of equations? What would happen if we obtained an equation with
an infinite number of variables w.r.t. the final semantics for the database pro-
cesses, and why, fortunately, it cannot happen in our database mapping frame-
work? Why do we need the flattening of a system of equations obtained by
the DB-process algorithm
DBprog
? How can we define the equivalence classes
