Re: Atomic Structures
Date: Wed, 20 Jan 2016 14:49:05 -0800 (PST)
Message-ID: <07d04cf4-8bef-46db-bdb3-7093401dec5a_at_googlegroups.com>
In this post I would like to give a few concrete examples, which can not be resolved by applying 6NF.
1.
In one of my post I wrote that 6NF can not solve the relations that
represent some relationship between entities. Note that relationships can be
extremely complicated.
Relationship must not be just between the two entities. Relationships may be
between 2, 3, or in general case between n entities. Note also that in some
relationsihps may participate in another relarionship.
2.
The following example, I have made on this user group. This example was used
in the application of 6NF in Anchor Modeling.
Here, this example is presented only in relation to 6NF. It is also
presented the use of, several of entirely new theoretical approaches in my
solutions.
As I have said many times, 6NF does not have real solutions, at all. I mean
a concrete solution, which brings a relation to the corresponding atomic
structure.
In my opinion, here essence is not in the normal forms. Here is the
following essential question: what are the building blocks for data and
sentences? Here I would add Frege's idea that "Sentences express thoughts".
The following example clearly shows that 6NF can not make atomic structure.
Here is the example:
I will use my example from 2005. See my paper "Some ideas about a new Data Model", Example 2.5 at http://www.dbdesign10.com The detail explanation regarding this example you can see in the abovementioned paper.
In this example I presented just one atomic relation. However, it should be understood in this example, that we have an entity and this atomic relation is just one among the others atomic relations of this entity.
Note that this my paper was "severely" discussed on this user group, for several years. Anyone can see this discussion.
Example for atomic structure:
The table Savings has only two attributes: Amount and AmountKey. The second
attribute is the primary key. The table is simplified for the purpose paying
attention to creating knowledge. Usually we create a table like this:
(i)
AmountKey Amount
...
116 $2000.00
...
However if we want to implement knowledge on the level of a value of the attribute
Amount, then we can, for example add six new columns in this table: Date1,
Date2,
Operater1, Date3, Date4, Operater2. (These 6 new columns represent knowledge
of the attribute "Amount". Knowledge of the attribute I have defined in my
papers.)
Table Saving now can look like:
AmountKey Amount Date1 Date2 Operator1 Date3 Date4 Operator2
...
116 $2000.00 5/Oct/04 1 John Mayell 6/Oct/04 1 Paul Jones 117 $2000.00 5/Oct/04 28/Oct/04 Mick Smith 6/Oct/04 29/Oct/04 Lee Evans 118 $2500.00 28/Oct/04 1 Mick Smith 29/Oct/04 1 Lee Evans
End of the example
My main structure from the above example have the following forms
(identifier-of-state, one-attribute, knowledge). Note that this my example
was presented in my paper in 2005.
Note also that above example has the following data structure:
(AmountKey, Amount, Date1, Date2, Operator1, Date3, Date4, Operator2).
This example present the new theory for databases, the new database design and the new way of aplication for databases.
3.
Frege's theory of types
In some of my posts, I noted that today a number of theorists developing the theory of types just based on Frege's system. Given that people are familiar with the story that B. Russell is the creator of Type theory, which he formed because of the discovery of paradox in Frege's theory, then this statement on Frege's Type theory seems odd.
Frege's types I'm going to expose the way, how it did John P. Burgess. In my
opinion, the best approach to Frege's work, is the way, how it did Burgess.
Moreover, I think that Burgess' approach should be included in textbooks,
because these are the most important results in mathematics and philosophy.
His book "Fixing Frege", I think it finally explained most of Frege's ideas
in the right way.
In my opinion, there is a lot of misunderstanding about Frege's theories.
One reason is the great complexity of Frege's theory. However, I think the
other reason is the subjectivity of some scientists rather than objectivity.
Of course this is my personal opinion.
Burgess writes, that he "... the ruthlessly modernized" notation of Frege's system. Now I'll start with Frege's types. I'll write a very brief about this, so that one can get an idea of what it is about here.
Frege introduces "saturated" and "unsaturated" expressions.
(i) Saturated expressions
Frege puts "names" and "sentences" in saturated expression. Burgess uses N
and S as labels for names and sentences. Since Frege works with names and
sentences, then it is clear why Burgess calls it "grammatical types".
(ii) Unsaturated expressions
Frege also introduces unsaturated expressions. Unsaturated expressions have
one or more gaps. If they filled in with expressions of appropriate types,
they would produce expressions Those that produce expressions of type S will
be called "predicates". And that is what interests us in relational
databases. (relational predicates). Further, Burgess uses certain notations,
that emerged later, after Frege's. Thus Burgess introduced predicate of type
S / T 1, ..., Tk, wherein S, T1, T2, ..., Tk are types.
There are many types of unsaturated expressions.( higher predicates ). For further research, mentioned book of J. Burgess, should be used. Frege introduces semantics. Thus, for example, Frege defines the following:
(1) The referents of expressions of types S/... are concepts. In other words
the referents of predicates are concepts.
(2) The referent of type N is the object which has the name.
Now I can make a few conclusions. These conclusions are related to Codd's types and Date & Darwen types. Note that Date & Darwen book about the Third Manifest has the following title: "Databases, Types and the Relational Model". The authors even put the word "type" in the title.
- Frege's system actually implies and determines the corresponding Type theory. However the depth of Frege's work is much larger than type theory, to mention just semantics and logic. As far as I know Frege did not use the term type. However types and hierarchy of types arising from Frege's system, determines very complex types, which have a semantics. I also have to say, that in this post, I presented only the beginning of Burgess's book. So this book requires a lot of work.
- In the first post of this thread, I presented Godel's approach to type theory, which is based on an entity, relationships and properties. Both of these approaches (Frege's and Godel's) are much stronger than Codd's "entity-type" approach. The relationship between Godel's approach and Frege's approach is very important.
Vladimir Odrljin Received on Wed Jan 20 2016 - 23:49:05 CET