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is well known that the logic negation as an antitonic truth operator, and hence
cannot be used in order to obtain the solutions for the schema mappings by
using standard fix-point semantics. How we can overcome such a problem by
the many-valued logics where we also use incomplete (unknown) information?
4. Are the provided algorithms for transformation of logic formulae (tgds) into
the algebraic (operad's based) expressions able to deal with the logic negation
operators as well? Is there any example presented in this chapter where we need
negation logic operators, and, if so, why?
5. Why it is important to express the integrity constraints over the database
schemas as a kind of the schema mappings? What is main difference be-
tween such integrity-mappings and standard inter-schema mappings based on
the tgds? Are the integrity-constraint mappings important for the composition
of the mappings? If not then explain why and which “trick” was used in order
to make an effective separation of them and of inter-schema mappings. Do we
have other technical possibilities to obtain an analogous result and compare it
with the method proposed here?
6. Why are we using the typed operads as an effective algebraic language in or-
der to provide the “algebraization” of the SOtgds logics used for the schema
mappings? What is the difference of such an operad's algebra and the standard
algebraic semantics presented in the introduction? What are the main operations
in the operad's algebra? Can you reformulate the operad's algebra by the ordi-
nary semantics of algebras and their operators, in the way as it was done with
the category theory in Sect.
1.5.1
?
7. What is the main reason for a definition of the semantics of the schema map-
pings in Definition
11
, based on the Tarski's FOL semantics? Does this defini-
tion extend the FOL semantics into the Second Order Semantics for the tgds?
Why did we introduce the negation operators in this method, if we did not use
the logic negation in the tgds? Can we use this semantics of the mappings for
the tgds with the queries that are using the logic negation operator as well? Try
to elaborate such an extension and show some simple example.
8. An Abstract Data-Object is a basic concept for the observational point of view
where the resulting relation (a view), obtained for a given query, is seen as an
observation of the information contained in a given database instance. What
is the relationship between the power-view database
TA
obtained as the (also
infinite) set of observations on a given instance database
A
, with the syntax of
the used query-language? If we are using the SQL for the relational databases
then we obtain
A
⊆
TA
. Is this power-view operator
T
a monotonic operator,
and, if it is, what is the reason for it? What do we obtain if we apply the operator
T
to the instance database
TA
?
9. What is intuitively the strict semantics of the schema mappings? Do we need
it in a special case of the Data exchange setting, and if not, is it the main gen-
eralization of the Data exchange setting? Is the information flux a database as
well, and can it contain the data which are not provided by the source database
of a composed mapping with a number of the intermediate databases between
the source and target database? If an atomic-data in an RDB database
A
is any
