Equivalence of Databases (Notion of)?

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Discussion Overview

The discussion centers around the concept of equivalence between two databases, D1 and D2, particularly in the context of their structural and functional similarities. Participants explore whether there exists a term or notion in database theory analogous to "isomorphic" in mathematics that could define when two databases are considered "the same." The scope includes theoretical aspects of database schemas and functionality.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions if the term "same" refers to identical schemas but different datasets, noting that there is no direct equivalent to isomorphic in relational database theory.
  • Another participant argues that if such a term existed, it would lack significant meaning due to the variability in data functionality based on reporting requirements and usage patterns.
  • A further contribution suggests that isomorphisms typically preserve part of a structure, implying that a potential definition of isomorphism in databases would maintain the schema but not necessarily the content or semantics.
  • There is an inquiry about methods for comparing the semantics or content of different databases, indicating a desire for deeper exploration of this aspect.
  • A clarification is made regarding the attribution of a previous response, correcting the name of the participant who replied.

Areas of Agreement / Disagreement

Participants express differing views on the existence and significance of a term analogous to "isomorphic" in database theory. The discussion remains unresolved, with no consensus on the terminology or the implications of database equivalence.

Contextual Notes

Limitations include the lack of a clear definition for the proposed notion of equivalence and the dependence on interpretations of structure, content, and semantics in databases.

WWGD
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Hi All,
Say we have two databases D1, D2, with the same number of entities and with equal functionality diagrams
(i.e., the functional dependence graphs are graph-isomorphic). Is there a notion in database under which D1, D2 are considered to be "the same" database , or some term equivalent to the same, as in the term "isomorphic" in Mathematics?
 
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Do you mean the "same" schemas, just a different data set? AFAIK there is no really analogous term in relational db theory to isomorphic. And if such a thing existed it would not convey very much meaning. Data in a db changes its functionality due to different requirements for data reporting, for example. We have differing indexes and code hints (for SQL queries in db's with identical schema owners), but because of use patterns (indexes, etc.) are actually different. If this were not true DBA's would be out of work. OR have a lot less to do at any rate.
 
Thanks, DH. But isomorphisms most often refer to the preservation of part of the structure, and not all of its aspects, i.e., we can have the Reals be isomorphic to some other set as a group, field, as an ordered field, etc. So I guess the isomorphism here would (it it was defined) preserve the schema, though not necessarily the contents or the semantic aspect. And , is there a way of comparing the semantics/content of different dbs?
 
WWGD said:
Thanks, DH.
Um, that was jim mcnamara who replied, not D H.
 

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