Atomic Structures
Date: Tue, 8 Dec 2015 10:54:51 -0800 (PST)
Message-ID: <0e11d8bf-79ff-40e1-b4d9-ce681ff11afd_at_googlegroups.com>
I would like to put this topic on the discussion because it has never been seriously analyzed in this group. The theme is one of the most important, because Atomic structures provide a variety of important solutions for databases. Atomic structures are also of great importance in some other areas, such as the atomic propositions and atomic predicate, they are also related to atomic concepts and atomic facts.
- RM / T
(i) Codd's solution does not provide anything new. Codd's solution does not
provide anything new. It was clear that the atomic structure consists of one attribute and key. The key has to be simple. If the key is not simple then we have no the atomic structure. Codd has introduced a surrogate key and "P-relations". This P-relation is the atomic structure consisting of a surrogate key and attribute, ie just as it is written above in (a). So we all know it and here Codd did not give anything new. But what is important here only, that Codd did not do. He has not shown how to construct the decomposition of an entity to its atomic structure. What is most important in this issue, it is the following question: what kind of a theory for the atomic structures need to build. Note that we have discussed the P-relations that have only one attribute. But by Codd's definition of P-relations, they can have one or more than one attribute. In RM / T, section 7, Codd defines P-relations as follows:
The immediate (single-valued) properties of an entity type are represented as distinctly named attributes of one or more property-defining relations, called P-relations.
Note that the P-relations, which have more than one attribute, are not the atomic structures. I'm not going to mention that we can add dates, intervals of dates and much more to these attributes. In such cases, P-relations do not seem as atomic structures, at all.
Note that normal forms can not lead to atomic structures. NFs are oriented
more at FDS, than at the atomic structures. Atomic structure are
fundamental, because they build other structures.
Note that normal forms can not lead to atomic structures. NFs are oriented
more toward functional dependencies, than toward the atomic structures.
Atomic structures are fundamental structures, because atomic structures
build other structures.
(ii) I will mention here three major groups of problems that RM / T can not
solve:
- In RM / T are not solved states of entities and relationships, nor
are states been noticed.
Note that only by using the states, we can get the right solutions
for the "history" and
for what I call "theory of general databases".
- RM / T also can not solve the databases that maintain "current
states".
- RM / T can not solve the databases that are supported by the
Internet.
- RM / T can not solve the problem of wrong data. Note that in big
computer centers, there is
department that corrects data on a daily basis.
I wrote about these problems on this user group and gave examples so that it does not make sense to write in detail again. These examples I showed when I talked about the failures in "Anchor Modeling. Note that the "Anchor Modeling" is better solution than RM / T, because it does not have "invisible surrogate". It also has a better key then Codd's RM / T.
(iii) Codd has introduced the "invisible" surrogate key. In my opinion Codd
realized that some problems he can not solve and that's why he
introduced this invisible key. In section 4, Codd wrote:
===============================================================
„Database users may cause the system to generate or delete a
surrogate, but they have no control over its value, nor is its value
ever displayed to them.“
==============================================================
Note that invisible surrogate key is not the way in which it is
possible to work at the following levels:
- at the level of the SQL language
- at the level of the design of database
- at the level of the database theory
(iv) Finally, I will mention another problem, which is a theoretical
character. E. Codd used two models in RM / T. These are the ER model and
relational model. It seems to me that Codd was not aware of this fact.If he
uses two models, then he has to define the mapping (say f), from the ER
Model into Relational Model. Also, he must determine the inverse mapping of
f (say g).
Let me quotes Codd, see RM / T, section 7: „Each P-relation has as its primary key an E-attribute whose main function is to tie the properties of each entity to the assertion of its existence in the E-relation. Each surrogate appearing in this E-attribute uniquely identifies the entity being described. Furthermore, it uniquely identifies the tuple of which it is part because the properties are single valued.“
We notice that in this quote Codd mixes relations and entities, and with them he was doing all together.
At the very least it is necessary to provide a definition of the entity. This definition Codd did not do.
At the beginning of this section 7, Codd says:
„We have seen that E-relation for a given entity type asserts the existence
of those entities having that type.“ So Codd introduced „Entity type“.
First, it seems to me Codd does not differentiate between data-type and
type. Data-type was introduced in software solutions. Type Theory is much
more general.
The other more important thing here is that the "entity" is the most general
category and that is a fundamental element in the design of the database.
Therefore, resolving entities as technical issues, is the wrong approach in
the most important elements in db design.
The following text, I have already presented at this group. This was done to show that priority of idea for entity / relationship model, does not belong to P. Chen. Now this article I present in order to show a better approach towards type than Codd's "entity type".
In 1944, Kurt Godel gave the following definition of the "theory of simple
types" :
By the theory of simple types I mean the doctrine which says that the
objects of thought (or, in another interpretation, the symbolic expressions)
are divided into types, namely: individuals, properties of individuals,
relations between individuals, properties of such relations, etc. (with a
similar hierarchy for extensions), and that sentences of the form: " a has
the property φ ", " b bears the relation R to c ", etc. are meaningless, if
a, b, c, R, φ are not of types fitting together. Mixed types (such as
classes containing individuals and classes as elements) and therefore also
transfinite types (such as the class of all classes of finite types) are
excluded. That the theory of simple types suffices for avoiding also the
epistemological paradoxes is shown by a closer analysis of these. (Cf.
Ramsey 1926 and Tarski 1935, p. 399)."
Codd actually working with the data types. I think it's wrong to work about the entity as a data type, when we do an entity, at conceptual level.
In my opinion Godel's and Frege's approach is a good approach. A number of mathematicians claimed that it was G. Frege who first did a good theory of types, and that it follows as a consequence from Frege's work.
It should be said that at theory of Simple type were worked following mathematicians: R. Carnap, F. Ramsey, W.V.O. Quine, A. Tarski and Alonzo Church.
So, in my opinion RM / T is on unacceptable theoretical level. RM / T can not solve some big areas of database theory and practice.
2.
I recently noticed an example that applies the RM / T. This example is from
the book: „Database design & Relational theory Normal Forms & Relational
Theory“ by C.J.Date.
This example uses known Relvar S that denotes suppliers. I hope that everyone is familiar with this working example, which is used in most books of C.J. Date, and is quite analyzed over the years on this user group.
Relvar S may be presented by the following scheme: { SNO, SNAME, CITY, STATUS} In this example, C.J.Date applies RM / T on this well known example and he obtain a design that looks like these four relvars:
S { SNO }
KEY { SNO } ;
SN { SNO , SNAME }
KEY { SNO }
FOREIGN KEY { SNO } REFERENCES S
ST { SNO , STATUS }
KEY { SNO }
FOREIGN KEY { SNO } REFERENCES S
SC { SNO , CITY }
KEY { SNO }
FOREIGN KEY { SNO } REFERENCES S
The complete example you can find at example 6, Chapter 15, pages 183 and
184
I don't think that this design is good. Note that SNO is not "invisible", as it should be in RM / T. Even more SNO is not surrogate, because, it is the real attribute from the real world. (SNO is supplier number, which every supplier knows, just as every supplier knows its name).
Even that "SNO" is "visible" surrogate, this C. Date solution is wrong and can not solve databases that belonging to large groups, which I have presented in this post at 1, under (ii).
3.
In 2005, I presented the solution for databases that uses only identifiers
for the keys. So, keys are not constructed exclusively using attributes. In
this solution, I introduced the identifiers of entities and relationships. I
introduced, also identifiers of states of entities and relationships. This
is the first time that all the keys are made via identifiers. This solution
can be seen at http://www.dbdesign10.com and also at
http://www.dbdesign11.com. This solution also was presented to this user
group, 10 years ago, on September 23, 2005. The name of thread is "Database
design, Keys and some other things." Later, I developed a theory of
identification, which fully describes the surrogates, and other identifiers.
In my discussion with Derek, I explained the aspects that are relate to
operations to a memory, the memory operations are related to surrogates
keys.
A particular problem was to work with atomic structures and the
corresponding theory to identifiers. Note that the atomic structures imply
atomic propositions in logic and atomic predicates in logic. The special
question is about atomic concepts. I will only mention some facts regarding
the concepts. Concepts are related to Theory of Mind, Frege's set theory is
based on the concepts and also the theory of predicates. From Frege's
definition of the concepts and its extensions can be derived first two
axioms of set theory (called comprehension and extensionality for sets).
In my work from 2009 atomic concepts were developed. So, I want to emphasize
the importance of atomic structures and ambitions of the authors of RM / T
and 6NF.
Vladimir Odrljin Received on Tue Dec 08 2015 - 19:54:51 CET