Re: Atomic Structures
Date: Wed, 27 Jan 2016 16:56:50 -0800 (PST)
Message-ID: <4a137c00-d708-44fc-b50e-68da9cf78ecd_at_googlegroups.com>
With this post, I'd finished this topic about atomic structures. In this
thread I showed that
RM / T and 6NF do not have theoretical significance.
The atomic structures are very important part of the theory, even one might
say that atomic structures are one of the most important issues in database
theory. Since the atomic data structures are linked with atomic
propositions, atomic predicates, atomic relations, atomic concepts, atomic
facts, atomic sets, then they have additional importance.
Regarding the construction of these atomic structures, I've done my solution. On this user group this my solution is discussed in detail and quite long. Therefore, I believe that my solution is good. Of course, if someone has questions or critical remarks, he is welcome. I'll try to give an answer to each question.
The theory of atomic data structures is done and presented only by my solutions. These my solutions are presented on this user group and on my websites:
http://www.dbdesign10.com and http://www.dbdesign11.com
These solutions enable the introduction of atomic propositions, atomic predicates, atomic relations, atomic facts, atomic concepts and atomic events.
These solutions are correct solutions. When I say correct solutions, then I think that these solutions are both theoretically and practically correct and effective.
This theory is with a lot of detail and it is impossible to describe in one thread all the details of my solutions. So I'm going to present a very short form of my data model, my solutions and only the most important parts. Otherwise, if someone wants to get into the details of my solutions, then you can find my papers on my websites. You can use my posts on this user group.
My first step is "Entity Relationship" model. The initial results of this model are made by a group of mathematicians and I have several times presented this approach using the article from K. Godel, from 1944. Among other things, this group of mathematicians using Type theory.
My second step is the introduction of Frege's theory. In my paper from 2008
I introduced the concepts and extensions of concepts in solving databases.
To my knowledge, this is the first time that someone has introduced concepts
and sets (extensions), as it is defined by Frege, in the design phase of
databases.
It is known that Frege's concepts were disputed because of Russell's
paradox. I have tried to solve Russell's paradox. My solution is presented
at this group. It seems to me that my solution of Russell's paradox is
substantially more general solution than Russell's.
I have to say here, that at this stage of database design, E. Codd made a big mistake. He did not mention the concepts at all. However concepts are the basis of Frege's approach. Relations are just part of Frege's system.
Note that Peter Chen, author of the Entity-relationship data model, does not define the concept (in his paper). I write this because today the ER model is like the father of Conceptual Modeling. However P. Chen mentions predicates, also E. Codd did it. Note that by Frege's definition, predicates denote concepts.
On the other hand E. Codd is the first, who made database model as a pure mathematical model. It is based on the relations and it is a significant step forward.
In this second step, I construct the link between theory of concepts and the theory of identification. This was done in my paper from 2008, see formula (3.3.3). This linking is more general than the concepts and it provides the solution of Russell's paradox.
My third step in the development of a database is the application of Leibniz's Law. Significant improvement of Leibniz's Law, is done by A. Tarski. Certain small improvements of the law were made by B. Russell and K. Godel. I also did some extension of Leibniz's Law. My first extension of Leibniz's Law is that it should apply extrinsic attributes (in addition to intrinsic attributes). Note that the database theory uses exclusively intrinsic properties of entities. My second extension of Leibniz's Law is that it does not apply to the entities, but to states of entities. Here it is necessary to introduce concepts that work with states of entities, rather than just with entities. My third extension of Leibniz's Law is the introduction of the theory of identification of objects..
The fourth step in my approach is the introduction of states. So I do not
work with the entities and relationships but with the states of entities and
relationships. When working with states, it is necessary to introduce a
number of new things. I will only mention two things. The first is that I
was able to formalize the work with the states. I've made it, by introducing
identifiers of states.
The second thing was consequence of a much deeper problem. This problem, in
short can be presented as follows.
People have always held that a name denotes a certain entity, although this
entity has been changed many times. But the following problem has always
existed: How an entity which has changed to another entity is, in fact, the
same entity.
This problem is solved in my paper. In my paper I gave the corresponding
procedures, constructions and semantics for solving this problem. This
problem is solved by the following procedure (a):
(a)
The main part of solving "temporal", "historical" and other complex databases consists of two sub-steps:
1. Constructing an identifier of an entity or relationship. 2. Connecting all changes of states of one entity (or relationship) to the identifier of this entity (or relationship).
I believe that the reason complex databases and databases of a general character have not been solved until now is because no one came up with that in part (a). Of course, the procedure (a) is only part of a series of things that allows to create a database of general character. The mentioned solution is important also for others fields, for example for philosophy, logic and semantics. (see for example: Ship of Theseus ).
My solution is event oriented. In my database model there are only two
events:
Event when new data is created.
Event when some data has ceased to exist.
So my databases are not "Temporal databases". I have defined the time by
using these two mentioned events.
Here I think on two system's events. Of course, there may be various other
events that are not these two system's events, but events that are related
to business application.
In my theory of databases, there is only one operation with data. This operation is "add", which adds new data to the database. There are no operations "insert" and "update."
In my theory about databases I have defined abstract objects.
Theory about identification is introduced completely in my theory about
databases. I think it's in databases entirely new theory.
In this theory, I solve the identification of abstract objects and the
identification of real objects.
In my paper from 2005, you can notice that all the keys are made as
identifiers. This approach, and this solution was first done in this my
paper. I want to emphasize that this paper is not using some simple keys,
this paper has the most complex databases with the most complex keys.
Identifiers are significantly different from the keys from the existing
theory of databases, in which the keys are constructed by using the
attributes. This paper is presented in this group. Discussion regarding this
paper started in September 2005 and caused quite a long discussion.
In my opinion, my theory of identification is important because it sets some
basic things.
I explained in many details my theory of identification, in my discussion
with Derek. It was in the following threads: "some information about anchor
modeling in 2013" and "The anatomy of plagiarism that was made by authors of
"Anchor Modeling"
For example in this discussion I clearly explained my identifiers of
entities: For entities in the real world there are three types of
identifiers of entities:
1. Surrogates (note that surrogates can identify an entity in database, but
surrogates can not directly identify the corresponding entity in the real
world.)
2. Identifiers that are locally defined
3. Identifiers that are international standards
I also explained that there are identifiers of abstract objects. For example, identifiers of states of entities are identifiers of abstract objects. Because the state is an abstract object. However there is always one atomic structure in which there are both: an identifier of an entity and the identifier of the state of the entity. So the identifier of the state of the entity is abstract object. But the identifier of the entity makes the identifier of the state of the entity very real.
Roughly speaking, the identification I defined recursively:
(i) attributes are identifiers.
(ii) entities are constructed from attributes (therefore the identification
of an entity is determined by using identification of entities'
attributes.
(iii) relationships are constructed from the the entities or from known
relationships...
By using my theory of identification, I gave the solution Russell's paradox. Very roughly speaking I solved Russell paradox by using two constructions. One of these construction is a "concept" and the other is the "identification".
The concept was introduced by Frege and a concept serve to determine the corresponding plurality. This plurality is understood as one object. The identification enables that each object from the mentioned plurality can be identified.
So mistake was that it was determined only a plurality. But the identification of objects belonging to the plurality, was not done. Note that the object which we want to identify, must exist.
If the matter is based only on the concept, then it is possible to construct a paradox. In short, the construction of the set depends not only on "conceptual thinking", it also depends on our capacity to identify individual objects.
Note that there are real (physical) objects and abstract objects.
My general database can be expanded into a complete database, that I call
"world".
This database in addition to the present and the past, also keeps and
maintains the future. The future is stored in the database as follows: The
database keeps a set of programs. More precisely databases keeps the states
of programs. By execution of a state of a program we implement the
corresponding future state.
I recently defined the conceptual data model based on set theory. This you can see in my threads: "Conceptual model based on set theory" and " A new way for the foundation of set theory"
Vladimir Odrljin Received on Thu Jan 28 2016 - 01:56:50 CET