Evolution mapping

Figure 19.11 Phase maps f(x, y) of a 6x4/um region of a fatigued FeCap (108 cycles) after negative (left) and positive (right) poling and evolution map of the piezoelectric phase signal f(x, E) (central picture) under varying (triangular shape) electric field E of the horizontal line indicated by the horizontal arrows. PI, P2, LI and L2 are discussed in detail later.

Powerful schema evolution infrastructure The comprehensive support for schema evolution discussed before requires a set of powerful and easily usable tools, in particular to determine the impact of intended changes, to specify incremental changes, to determine Diff evolution mappings, and to perform the specified changes on the schemas, instances, mappings, and related schemas. 

Description/focus of Commercial Commercial Commercial Evolution mapping Propagation of Conceptual... 

Commercial DBMS do not support abstract schema mappings but only SQL for specifying view mappings and evolution mappings. There is no support for multiple explicit schema and database versions. Once the DDL statements of an evolution step have been executed, the previous version of the evolved objects is gone. There is no support for applications that were developed against previous versions of the database. 

Specification (incremental, new schema) Evolution mapping (2) Incremental or specification of new ontology version (2) Incremental... 

Hartung M, Gross A, Rahm E (2010) Rule-based determination of Diff evolution mappings between ontology versions. Technical report, University of Leipzig Hick JM, Hainaut JL (2006) Database application evolution a transformational approach. Data Knowl Eng 59(3) 534-558... 

M, where the target schema of M is the source schema of M. The result is a schema mapping M o M that has the same effect as applying first M and then M. For our schema evolution context, M o M combines the original transformation M with the evolution mapping M . 

Let us assume that the target schema evolves to a new schema T consisting of one relation Takes that combines all the attributes in T (i.e., sid, ma j or, course) and further includes an extra grade attribute. Moreover, assume that the evolution mapping from T to T is ... 

For our running example, to adapt the above mapping Al to the new target schema, we must compose Al with the evolution mapping Al. As it turns out,... 

Observe that the self-join on Takes in the above composition is needed. This can be traced to the fact that students can have multiple majors, in general. At the same time, the Takes relation need not list all combinations of maj or and course for a given sid. However, the evolution mapping M requires all such combinations. The composition M o M correctly accounts for all these subtle semantic aspects. To see a concrete example, consider the following instance of Takes ... 

Thus, in the new schema, the relation Manager of T is intended to be a copy of the relation Reports of T, while the relation Sel fMgr is intended to contain all employees who are their own managers, that is, employees for which the eid field equals the mgr field in the relation Reports of T. Note that the evolution mapping M is a GAV mapping. 

Additionally, the above theorem also applies in the context of source schema evolution, provided that the source evolution mapping M" has a chase-inverse. We summarize the applicability of Theorem 3 to the context of schema evolution as follows. 

The important remaining restriction in the above corollary is that the source evolution mapping M" must have a chase-inverse and, in particular, that M" is a lossless mapping. We address next the case where M" is lossy and, hence, a chase-inverse does not exist. 

We consider a variation of the scenario described in Fig. 7.2. In this variation, the evolved source schema S" is changed so that it no longer contains the ma j or field. The new source evolution scenario is illustrated graphically in Fig. 7.4a. The source evolution mapping M" is now given as ... 

As it can be seen, the recovered source instance U is not homomorphically equivalent to the original source instance there is a homomorphism from U to 7, but no homomorphism can map the constant CS in 7 to the null X in U. Intuitively, there is information loss in the evolution mapping M", which does not export the major field. Later on, in Sect. 5.2, we will show that in fact M" has no chase-inverse thus, we cannot recover a homomorphically equivalent source instance. 

We also remark that the language needed to express quasi-inverses requires disjunction. As a result, PRISM uses an extension of the chase and backchase algorithm that is able to handle disjunctive dependencies this extension was developed as part of MARS [Deutsch and Tannen 2003], Finally, we note that we may not always succeed in finding equivalent reformulations, depending on the input query, the evolution mappings and also on the quasi-inverses that are chosen. Hence, PRISM must still rely on a human DBA to solve exceptions. 

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