Some ideas about a new Data Model

New York City, NY USA

Email:    vldm10@yahoo.com
Posted: September 17, 2005

1. Ordered pair (Conceptual Model, Logical Model)
A Conceptual Model is a domain in which a part of the Real World associated with subject knowledge is
represented.
This model, aside from Entities, Relationship, Attributes and Attributes’ values, has Events.
There are only two kinds of events in the Real World:
i)  An event which causes new information
ii) An event which causes some existing information to not be valid after this event. We
will also say this event closes information.
Here information is the meaning of the event in the Conceptual Model. A Conceptual Model has events
which correspond to events from the Real World. Here they can have only two values: N and C, they are
abbreviations for “new” and “close”.

1.1 Construction of Conceptual Model
We determine the Conceptual Model so that every entity and every relationship has only one attribute, all
of whose values are distinct. So this attribute doesn’t have two of the same values. We will call this
attribute the Identifier of the state of an entity or relationship. We will denote this attribute by the symbol
Ack. All other attributes can have values which are the same for some different members of an entity set
or a relationship set. Besides Ack, every entity has an attribute which is the Identifier of the entity or can
provide identification of the entity. This Identifier has one value for all the states of one entity or
relationship.
Like the Logical Model, here we will use the Relational Model, although the above is not limited to the
Relational Model.
An entity set and a relational set are mapped into relations of the Relation Model. Attributes from an entity
or relationship are mapped to the relation’s attributes. The events from Conceptual Model are mapped to
corresponding “new” and “close” events from the Relational Model.
Let’s denote by Ark the attribute in relation R which corresponds to the Ack. All the values of the attribute
Ark are unique.

1.2 Definition of key
The key K for relation R is the attribute Ark such that:
1. The key K uniquely determines a tuple in relation R and is the primary key.
2. One particular value of K provides identification for one state of the corresponding
entity (or the relationship)
3. Two or more of the key’s values from relation R, which are related to one
corresponding entity (relationship), provide better identification and meaning to
the entity (relationship).

This construction of entities and relationships enables corresponding relations to be almost normalized.
We don’t have compound keys, we have only one candidate key, and generally speaking, all the other
values that are not Ark’s can be repeated any number of times.

1.3 Example
Given the table Car

CarKey     CarID     Maker      Color     …

23             vin1        Buick        silver    …
24             vin1        Buick        blue     ...
25             vin1        Buick        red       …
26             vin2        Honda      silver    …
27             vin3        Ford         black    ...

Here the CarKey is the Identifier of the state of the entity Car and this is the only column of the table
which has unique values. So the attribute CarKey is the primary key.
Car ID is an Identifier of the entity Car. We use VIN values for this attribute.
Maker, Color,… are attributes of the table Car.
In this example the CarKey’s values 23, 24 and 25 denote three states of the one car identified with the
CarID = vin1. These states are determined with the car’s color.
We can see that the above definition of the key is satisfied:
1. Every value of the key is from the attribute CarKey. The CarKey is, in fact, the column
Akr and because of that it has unique values.
2. One particular value of the key is one state of the car. Value 23 defines the car as
silver, and value 24 describes the car’s color as blue.
3. The three values 23, 24, and 25 describe the car much better than one value. For some
purposes these three values are more meaningful (for example an investigation of a stolen car).
We can identify every car in the real World with the value of the CarID.

Now, let Person be the following table:

PersonKey  PersonID  PersonName   …

208              ssn1          Mary Jones     …
210              ssn2          John Stewart   …
…
Where PersonKey is an Identifier of the state of the entity Person,
PersonID is the Identifier of the entity Person,
PersonName is the name of the person.
Here Mrs. Mary Jones changed her last name because she had gotten married to Mr. Adams.

Let’s form the relationship Owner which corresponds to a person who is the owner of a car:
This relationship can have the following values

OwnerKey  Person Key  CarKey    Year
________________________________

54               210                26          2003
55               210                24          2004
56               210                26          2005
…

where OwnerKey is the Identifier of the state of the relationship Owner,
PersonKey is the Identifier of the state of the entity Person,
CarKey is the Identifier of the state of the entity Car, and year is the year of ownership.
Here Mr. John Stewart bought a Honda in 2003 and then he sold it to his friend.
He bought a Buick in 2004. In 2005 he again bought his old Honda from his friend.

2. Creating, representing and implementing knowledge in a database
(Posted September 22, 2005)

2.1 Categorizing of data
We will divide data into two categories
1. Derived data
Simply said, these data are not written into a database. They are obtained from existing  data in
the database. For example, these are data which we can get from a report, display, view, or query,
as well as data which we can get by applying operations on existing data in the database.
2. Data which get written into the database; they are new and can’t be derived from existing
data in the database. In this case the database will be changed. There are two kinds of these data:
i)  Data which are our own information and which we maintain.
ii) Data which are somebody else’s information and which somebody else sometimes maintains. But
we get these data from them and store the data into the database. These kinds of data are, for
example SSN, Address etc. It means that in this case there are multiple sources of knowledge
about a data. Similarly, pictures and multimedia information which are made by certain devices
have specifics sources of knowledge. For example a picture is made by a camera and stored
directly into a database.

The user can write in (enter) only two kinds of data into the database:
i)  new data i.e. data which is new in the database;
ii) data which have existed in the database as valid and which now have been announced invalid from
some point in the time i.e. these data are not current or existing anymore from some point of time.
We will call this – closing the current data or simply, closing.

Here the term data refers to a value that is stored in the database. We create the new data using the
Constructor. We close the data (closing) with the ClosingConstructor. These two constructors in some
way correspond to the Constructor and Destructor from OOP. The difference is that
ClosingConstructor doesn’t delete or destroy data; it just says that the data is not valid from some
point in the time. The second difference is that these constructors can be applied only to one data.
The third difference is that these two constructors are related (initiated) to events. There are only two
events in the database: event N and C. As it is earlier said, the first one is creating new data in the
database and the second is closing current data. Events N and C usually correspond to events in the
Real World. The forth Difference is that, using Constructor and ClosingConstructor, we create keys
and knowledge in the database.
Finally, these two constructors are user created i.e. they can vary from case to case. The event in the
Real World defines the state of an entity or relationship following this event.
The amount of knowledge which we will apply depends on us.

2.2 Knowledge related to the data and its representation in the database.
1. We will distinguish our knowledge from another’s and we will separately represent
these two in the database.
2. We will distinguish knowledge related to the data of the Real World from knowledge
related to the data of the Logical Model and we will separately represent these two in the database.

Knowledge about one particular data, i.e. about an attribute’s values, is represented by a set F of facts

F={F1,…,Fm}                 …  (1)

where F1, F2,…, Fm are facts about one particular data. This total knowledge about data consists of
knowledge related to the Real World and of  knowledge related to the Logical Model.

2.3 The representation of knowledge in the Conceptual Model
As stated in 1.1 one entity (similarly with a relationship) takes the form

(P,E, A1, … , An)          …   (2)

Where P is the Identifier of the state of the entity (relationship)
E is the Identifier of the entity
A1,…,An are attributes of an entity (relationship)
Each attribute, including E and P, can have different sets of knowledge F associated to them.
Thus
P has knowledge   Fp1, Fp2,…,Fpi
E has knowledge   Fe1, Fe2,…,Fej
A1 has knowledge F11, F12,…,F1k          …  (3)
.
.
.
An has knowledge Fn1,Fn2,…,Fns

Here, in the Conceptual Model we represent knowledge related to the Real World. Because the
Conceptual Model is an interpretation of the Real World, and because the Conceptual Model is mapped
to the Logical Model, here there is no knowledge related to data of the Logical Model.

2.4 The representation of knowledge in the Relational Model
In the Relational Model knowledge is represented by columns. An entity (2) can be represented in two
ways in the Relational Model.
1. As a relation R, plus additional columns of knowledge, all in one tuple for one member of  an
entity (relationship) set.

or

2. As a set of the following relations
i)  K-relations
(P,A1, F11,…,F1k,L11,…,L1p)                      …  (4)
.
.
.

(P, An, Fn1,…,Fns, Ln1,…,Lnq)

ii)  E-relation

(P, E, Fe1,…,Fej, Le1,…,Ler)                        …   (5)

iii)  S-relation

(P, E, Fp1,…,Fpi, Lp1,…,Lps)                       …  (6)

Here we have added knowledge related to the Logical Model and it is denoted by Lij. We also include
knowledge from Conceptual Model, here it is denoted by Fij.

Example 2.5
How to create, implement and represent knowledge related to the data in the database.
We will show this with the example of the data Amount from a Savings table. We will suppose that it is
possible to make a deposit by sending a check by mail. 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:

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.
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/)4         1         Mick Smith  29/Oct/)4          1         Lee Evans

These six columns are newly created knowledge about the Amount data. We could add more or less
than six columns; it depends on which level of knowledge representation we want. The first three
columns form a logical whole (unit) and are related to an event in the Real World regarding Amount.
The second three columns are also a logical whole but they are related to a corresponding event in
the database. Say that on 5/Oct/04 somebody deposits \$2000.00 (by mailing a check) into the
Savings account, and John Mayell receives the check and confirm this. The next day, 6/Oct/04,
Paul Jones enters these data into the database. On 28/Oct/04 somebody deposits \$500 dollars into
the account. Therefore, we will “close” the data about \$2000.00 and proclaim it not valid. In this case
this is done by entering 28/Oct/04 in Date2, that is, on this day in the Real World this data ceased to
exist as current (valid). This information was entered into the database the next day 29/Oct/04 by
Lee Evans, so this data is no longer valid in the database. The new value of \$2500.00 in column
Amount is now valid, starting from 29/Oct/04. Here the “1” (or any other specific value) in Date2
means that the data is current in the Real World. If  “1” is in Date4 then the data is valid (current)
in the Database.

The rows with key values of 116 and 118 were made by Constructor, while the row with the key value
of 117 was made by the ClosingConstructor. The values in Date3, Date4, and Operator2 are created
by the system. In fact, constructors get these values from the system and store them into the database.
Thus, here we have an example in which knowledge from two sources is associated to one value of the
attribute Amount. One of the sources comes from an operator in the Real World and the other one from
the system.

We see that the key has two roles: it is the primary key for the table Savings, that is, it makes differing
rows in the table. Secondly, out of the database, i.e. in the Real World, multiple values of this key help
us to determine the states, meanings, and knowledge of one entity’s  instance in the Real World.

Let us assume that now we have a table with more than two attributes. Now we can assign a different
number of columns of knowledge to each attribute. These columns can also be different, concerning
what they represent.

2.6 Solutions for two significant problems
This technique of implementing knowledge enables us to make solutions for certain problems of a
general character. Let’s look at following two problems.

Problem 1.
We need a solution such that it can, in a formal way, recognize who created the data and how it was
created, (for all its data). We can make this problem more complex. We can create a kind of game with
the end user in which the user’s goal is to “break” the database solution Let us allow the user to enter
in the database what he/she wants and  how many times he/she wants, without any limitations.
The end users utilize corresponding data entry screens.
The solution should recognize all actions which were done and show exactly who did it and how it was
done, without the help of programmer. For example, a manager who doesn't know programing can control
many aspects of data on a his screen. This is important in case we need to know how a fault was
created and who is responsible for it. This is also a solution for malpractice of the database. It also
enables us to sell the database solution and maintain it easily. The above Example 2.5 is a good way
to solve this problem.

Problem 2.
To solve problems with TransRelational Model.
In this model columns of relation are stored separately. If we want to access more then one attribute of a
given record we have to know how to rebuild the “record”. To make this problem more general, we can try
to solve it using an entity with all its states. This problem has a very simple solution that uses a query,
knowledge columns and the E-Relation. We can also display a "record" in many different shapes and
meanings. We can also display one entity's instance as all of its states.
3. About Some explanations and notes related to
chapters 1 and 2
(Posted January 9, 2006)

I wrote these explanations and notes during the discussion which was about the data model presented in chapters 1
and 2. The discussion took place on September / October 2005 in the user group Comp.Databases.Theory. I
believe that these notes can be useful for practical usage in applications and as additional explanations for some
topics in this data model

3.1 Regarding the Conceptual Model I defined it as a product of both objectivity and subjectivity , i.e., the
Conceptual Model is related to both the world and to the subject who interprets (a part of) the world. So concepts
deal with the real world and with a subject’s view of it. Knowledge also is involved in this functionality.

3.2 During the construction of the Conceptual Model two things among others should be considered:
(i) The identifier of an entity (relationship)
(ii) The identifier of the state of an entity (relationship).

Every time an attribute of an entity or relationship is changed we will create a new identifier of the state of an entity
or relationship. But this working definition which uses the term “change of the attributes” is not real and it is not
precise. We will determine the event from the real world which causes the change of an attribute’s value i.e., change
of the corresponding state of the entity (relationship). So in the case that an entity (relationship) is changed we will
create a new identifier of the state which corresponds to the real world event, which causes this change.
This technique can be very useful if we want to associate knowledge with data.
As a database is more complex this model becomes more effective.
For example, if a water supply is closed twice for three hours during one day, we would create two new identifiers of
state. They correspond to the two mentioned events of this relationship. An appropriate office or department will add
necessary documentation about these events. In this example our key is related to real world events and they are
externally verifiable by the documentation.
(If we use the usual solutions then we need a compound key with the following “attributes”: address of building,
address of the water meter (water meter can be in another street), date and time. We can notice that date has three
“subfields” - day, month, and year. The time also has three “subfields”. An address has five “subfields” and we have
Is date an attribute of some entity or relationship?  We should be aware that a date is based on the ratio of two
different paths of Earth, with some corrections. Time corresponds to the earth’s path around itself)

3.3 The knowledge about data is defined as a set of facts about one particular data. Here the data is an attribute’s
value. An entity or relationship also can have their own facts.
The identifier of the state of an entity (relationship) also has the purpose of connecting knowledge about a data with
the data itself and its states.
Whenever the knowledge about a data is changed, we will assign a new identifier of the state of an entity or
relationship.
Example 2.5 shows how to connect the knowledge to corresponding data using the identifier of the state of an entity
(relationship).

3.4. The knowledge, the identifier of the state of an entity (relationship) and the identifier of an entity (relationship)
are optional. Their application in a particular database project depends on the complexity of the database, its
organization and business rules. If, for example, there are no changes of the attributes’ values then the identifier of
the state of an entity (relationship) is equal to identifier of an entity (relationship). The use of knowledge depends on
an application’s needs. Sometimes we don’t need any knowledge; sometimes the use of knowledge can be complex
involving relations and logic among facts.

data. Here facts are:

(i)   Permanent, i.e., they are memorized in a database;
(ii)  They are associated with one particular entity’s attribute value in the database;
(iii) The facts about one data can be from different sources;
(iv) The facts can be true, false or can be mistakes. The source of the facts can purposely
give false facts.
(v)  The set F of facts about a data, which is recorded in the database, can be a subset of
a set G of the facts, which has some additional facts about the data which are not
recorded in the database.

Here we are speaking only about the facts which we have in a database and which are the knowledge about one
particular attribute’s value from the database.

In a similar way we can define knowledge about an entity and relationship.

3.6 Regarding the definition of a key, the following should be satisfied:
(i)   Key determines a tuple. This means that the Key value in Relation Model enables
all the rows in a table to be different. This property of  Key is related to the
Relational Model.
(ii)   Key provides identification of an entity or relationship. Key does not always directly
identify an entity or relationship. In example 3.2 beside Key, we will use the
documentation or maybe some additional attributes and knowledge to identify the
relationship. Thus, generally speaking Key does not identify an entity
(relationship), rather we will say that Key provides an identification of an entity
(relationship). This property of Key is related to the real world.
(iii)  In the case that we have more states of one entity or relationship, Key enables us to
treat this set as one entity or relationship. This property of Key helps to
identify the entity in the real world and enables it a better meaning.

4.  What conditions must be satisfied in order for relational
schema R to be equal to the join of its corresponding
binary schemas?
(Posted May 15, 2006)

I will introduce several of well-known terms:
-   A key is simple if it consists of a single attribute.
-   Two or more attributes are mutually independent if none of them is functionally
dependent on any combination of the others.
Now, let R (K, A1, A2,…,An) be a relation schema, where
(a) key K is simple
(b) A1, A2,…, An are the nonkey attributes which are mutually independent
(c) R1 (K, A1),  R2 (K, A2), …, Rn (K, An) are the corresponding binary schemas.
We will say that relational schema R is equal to join of its corresponding binary
schemas and denote it as
R (K, A1, A2, …,An)   =   R1 (K, A1) join R2 (K, A2), join … join Rn (K, An)
if and only if every relation that is a legal value for R is equal to the join of its
corresponding binary relations.
(d)  R has a set of the associated integrity constraints.

4.1 Definition.
Relation schema R (K, A1, A2,…,An) is in Simple Form if R satisfies:
R (K, A1, A2, …,An)   =   R1 (K, A1) join R2 (K, A2), join … join Rn (K, An)
if and only if
1.     Key K is simple
2.     A1, A2,… , An  are mutually independent.

(In definition 4.1 the relations are joined using common column K.
Schema = (Sig, C) where Sig is a schema signature and C is a set of integrity constraint
expressed as sentences. Relational schema  R is related to one relation from the RM)
Simple Form says what we should to do in order to decompose a relation schema into
the join of its binary relation schemas. It says how to effectively make the column-based
representation of the relation (i.e. How to do this).
In fact Simple Form suggests that a “good” design starts at the conceptual level. The
design of an entity (relationship) should satisfy two conditions:
(a)        The construction of the key so that the key is simple.
(b)        The attributes of an entity (relationship) should to be mutually independent.
Of course this second condition is natural. The attributes of an entity (relationship)
in the real world are not mutually dependent.
The conditions for Simple Form, that the key is simple and that the attributes are
mutually independent, in fact mean that relation schema R is in 2NF, 3NF, BCNF,
5NF (PJ/NF) and that the relation is equal to the join of its binary relations.

4.2    The construction that makes every key simple
Now we have to solve the main problem: how to design the construction of the simple
key in order that this construction is universally applicable to every entity (relationship)?
This construction is shown in chapters 1 and 2, the key should be constructed according
to definition 1.2.

In chapters 1 and 2 all databases are divided into the following two groups:
(A) The databases in which changes to the entities (relationships) are maintained.
Every attribute of every entity (relationship) can be changed and the database
solution can maintain all states of the entities (relationships). These databases can
be very complex. They are solved by applying the identifier of the state of an entity
(relationship), the identifier of an entity (relationship) and according to
definition 1.2.
(B) The databases in which changes to the entities (relationships) are not maintained.
These databases exist in two forms.
(i)   All the entities (relationships) are unchangeable i.e. The entities and relationships
are same as the first time they were seen.
(ii)  There are the changes of an entity or relationship, but we keep only the most
recent updates, so they are same as the last time they were seen.
These (B) databases usually are simple but frequent in business. For these databases
we assume that the identifier of the state of an entity (relationship) is equal to the
identifier of an entity (relationship). In (B) case we will construct the simple key
that is in fact the identifier of the entity (relationship).

4.3    We can apply another approach to the binary relation schemas. We can use the
set of the mappings from entity E1 (K, A1,…,An)  to binary relational schemas
R1 (K, A1), R2 (K, A2), …, Rn (K, An). Now we do not have relational schema for
R (K, A1, A2,…,An), rather we have binary relational schemas R1 (K, A1), R2 (K, A2)
, …, Rn (K, An) in  Relational Model. Here we can derive every relation r, as the join
of the corresponding binary relations. We can do this using only one (join) operator
and key K. We can do this for all entities and relationships from Conceptual Model.

4.4    It is important to notice that E-relation or S-relation from 2.4 eliminates the
transitive functional dependencies. If we decompose a relation R into E-relation and
relation R1 (A1, … ,An-1), then R1 (A1, …¸An-1) does not have the transitive
dependencies, by its construction. E-relation (from 2.4) has great importance.
It defines the relationship between the identifier of the state of the entity (relationship)
and the identifier of the entity (relationship) i.e. It defines the relationship between
the identified entity (relationship) and its changes. The E-relation also improves the
meaning its intention and extension, involving the changes and knowledge of the
related and identified entity (relationship).

4.4    The conclusion
In chapters 1 and 2 it is shown how to effectively decompose arbitrary relation into
its binary relations and how to implement this procedure.
In chapter 4 it is shown which conditions a relation should to satisfy so that it can be
represented as join of its binary relations. These conditions also suggest the design
of an entity (relationship) and this conditions are in Simple Form.
Chapter 4 shows the decomposition without the knowledge columns. Chapter 5 will
consider decomposition that includes the knowledge columns.

5    The attributes, the facts and the states
In 2.2.2 knowledge about one particular data i.e. About one attribute’s value was
defined as follows:

5.1    Definition.
The knowledge about one attribute’s value is based on:
(i)     The set of the facts F = {F1,F2, … ,Fij).
(ii)    These facts are related to the relationships between one attribute and an
entity (relationship).

Now we will define an attribute of an entity (relationship).

5.2   Definition.
The attribute is represented by knowledge about an property.
This knowledge is based  on:
(i)     One fact.
(ii)    It is about one entity’s property.

5.3    We will call knowledge about attribute - primitive, because:
(i)      It is based on one fact.
(ii)     It is not derived from anything, but from which others are derived.
(iii)    It represents one particular property from the actual world.

We can notice the difference between knowledge about attribute and knowledge about
the attribute’s value. (in definitions 5.1 and 5.2)
(i)      Knowledge about the attribute’s value is based on the set of facts, while
knowledge about the entity’s property is based on only one fact.
(ii)    The first definition is about one attribute’s value while the second definition is

5.4    We also have the data about the entity as a whole. These data are common for
all attributes of one entity. They are based on the set of the facts.

5.5    Facts from 5.1 are related to one particular attribute. They are not the attributes or
the properties of the entity. The others concepts should be treated in the same way.
For example, time and date.

5.6   The State of an entity or relationship
The states are derived from the attributes and from knowledge about the attribute’s
values. We also defined the attributes as a kind of knowledge, which we named
primitive. Because of this we have the following definition:

5.7   Definition.

5.8    Definition.
A change of a state of an entity (relationship) is a change of the actual knowledge
about the corresponding entity (relationship). This change of the state of one
entity (relationship) is represented with the identifier of the state of an
entity (relationship)

5.9   The decomposition of relation schema R that has the knowledge columns
Let R (K, A1,F11,…,F1i,…,An,Fn1,…,Fnk) be a relation schema , where key K is
simple. A1,…,An, F11,…,Fnk are mutually independent attributes and  the
corresponding knowledge columns are also mutually independent by their
construction. However Fij are not primitive.
Then    R  =  R1 (K, A1, F11,…,F1i) join,…,join Rn (K, An, Fn1,…,Fnk) because K is
simple.  This join is in the sense of 4/c and 4.1.
E-relation or S-relation defined in 2.4 eliminates the possibilities that a key be
composite. If we decompose a relation R into E-relation and relation R0, then R0
doesn’t have a key that is composite. This is by the construction of R.
We can further apply this decomposition to the relations R1,…,Rn  - if we need it.

6   The Examples
(Posted November 22, 2007)

The examples are from my posts on user group comp.database.theory where I
discussed the ideas presented in this paper.
They are an addition for the explanation and help better understand what was
written in the paper.

6.1    Example
In the following example I will use the table Car, slightly altered from example 1.3,
and explain the construction of Simple Form, i.e. the construction of binary
relations.

Step1
--------
Table Car
CarKey     CarID     Maker      Type        Color    Datefrom      Dateto
------------------------------------------------------------------------------------------------

23             vin1        Buick       sedan      silver    1.1.2000.    12. 31. 2000
24             vin1        Buick       sedan      blue      1.1.2001       8.1.2001
25             vin1        Buick       sedan      red        8.2. 2001     1.1.2005
26             vin1        Buick       sedan      silver     1.2. 2005      999999
27             vin2        Honda     sedan      silver     3.15.2006     999999
28             vin3        Ford        sedan      black     3.15.2006     999999

999999 – represents the maximal date in the used software and means that the
corresponding data is current.
In this table, the columns Datefrom and Dateto are strictly related to one attribute
from the column Color. Datefrom and Dateto are not related to the entity Car.
Datefrom and Dateto are also not attributes. They are a part of our actual
knowledge about one particular attribute from the column Color.

The relation Car also represents knowledge about a particular attribute from the
column Color. Knowledge related to one particular attribute is defined in 2.3 and 2.4.
Therefore, besides columns which represent the attributes, the relation Car
also has columns which represent knowledge about attributes.
This construction of a relation which includes knowledge columns is determined
and defined by that which is stated in 1,  2.3 and 2.4.

Step2
---------

Now from the table Car I will construct the following four tables:

Table1                             Table2                            Table3
CarKey  CarID                CarKey   Maker                 CarKey    Type
-------------------               --------------------                  --------------------
…                                  …                                      …
23          vin1                   23          Buick                   23          sedan
24          vin1                   24          Buick                   24          sedan
25          vin1                   25          Buick                   25          sedan
26          vin1                   26          Buick                   26          sedan
27          vin2                   27          Honda                 27          sedan
28          vin3                   28          Ford                    28          sedan
…                                     …                                       …

Table4
CarKey     Color      DateFrom      DateTo
-------------------------------------------------------
…
23      silver      1.1.2000       12.31.2000
24       blue       1.1.2001       8.1.2001
25       red         8.2.2001      1.1.2005
26      silver      1.2.2005         999999
27      silver      3.15.2006       999999
28      black      3.15.2006      999999
…
Basically, here in Step2 I constructed four “column-based” or “attribute-based”
relations from the relation represented by the table Car in Step1. The first three
tables in fact have one column and key.
Table4, in addition, has knowledge about the property Color which is represented
by two columns (Datefrom and Dateto).
One can add some other “knowledge-columns” related to Color. Now in Step2
we have the relation Car from table1 represented in Simple Form.

6.1.1  How a Relation Should Be Constructed  in the General Case
Now, considering the above example, we can define the construction of a relation
in the process of the design of a database. The following description is for complex
databases whose entities and corresponding relations are defined in 2.3 and 2.4.

1. First, we will construct the entity. The construction of entity / relationship should
have:
(i)  A simple key
(ii) Mutually independent attributes
(iii) The attributes only from one entity / relationship, i.e. only its own attributes.
This condition can be derived from an entity’s definition and from 5.2.

2. Now that we have the entity, we will directly construct the corresponding binary
relations. The construction of the binary relations should be as it is done in Step2
in  6.1 example. So we do not need Step1. We can get the relation from Step1
using a “join” of the corresponding binary relations.  This construction of binary
relations is based on 2.3,  2.4 and on the set of mappings mentioned in 4.3.
These mappings are between set of entitis and the corresponding set of the
binary relations. This set of mappings gives the links between an entity represented
as the set of attributes i.e. the entity as the whole, on one side and the binary
relations between one entity’s attribute and the entity’s identifier on the other side.
Briefly in 4.3 there are links among an entity, the binary relations, the entity’s,
attributes, the states and the identifiers.
Now, when we have binary relations and their entities, we can define mapping
from binary relations to the entity’s instances. This mapping is determined by
key K.

We can notice that this design is based on the immediate construction of binary
relations rather than on the decomposition of a relation.

6.1.2     The Identifiers
In example 6.1 CarID is an identifier of the entity Car, and it is a VIN number.
CarKey is the identifier of the state of the entity Car.

- The identifier of an entity or relationship identifies the abstraction: entity, or
the abstraction: relationship. This identifier should also be used to identify the
corresponding real world object or relationship which we abstract.

- Similar to this is the identifier of the state of an entity or relationship – this
identifier identifies the abstraction: state of an entity, or the abstraction: state
of the relationship. The identifier of the state should also be used to identify
the state of the corresponding object (or relationship) from the real world.

- The group of identifiers of the state of an entity or relationship can be used to
provide  better identification and meaning to the entity or relationship. This is
explained in 3.6.

The identifier of the state of an entity or relationship is not created arbitrarily. It is
always initiated by a real world event, as is defined in 3.2.  This connection with a
real world event enables a company great possibility to create its own technology.
For instance, in the above example 6.1, a company can establish additional paper
documentation for any painting of a car, with customer signed agreement and many
other options – all this associated with the identifier of the state of the entity Car.
The identifier of the state of an entity or relationship always goes with the identifier
of an entity or relationship. In the above example the identifier 26 is tied with VIN1,
so it is not arbitrary at all.

Obviously, the different states correspond to the different identifiers of the state, and
vice versa.  There are no two same states of one entity / relationship.

6. 2   Example
In the following example I will consider more then two knowledge-columns related
to property Color.
Here I modified Table4 from 6.1 and added the six knowledge-column related to
the property Color: Datefrom1, Dateto1, Datefrom2, Dateto2, Operator1, Operator2.
So Table4 can have for example the following data:

Table  4
CarKey  Color  Datefrom1  Dateto1   Operator1   Datefrom2   Dateto2   Operator2
______________________________________________________________

23          silver   1.1.2000     999999        John         1.2.2000       999999      Mike
24          silver   1.1.2000   12.31.2000    Paul          1.2.2000      1.2.2001     Bill
25          blue     1.8.2001    999999         Bill            1.8.2001       999999      Bill

These six added columns have same role as it is in example 2.5.
However here in example 6.2. is shown link between whole relation Car and the
relation represented with Table4. Regarding 2.3 and 2.4 we can associate arbitrary
number of knowledge-columns to every binary relation, including E-relation.
Off course when we add knowledge-columns to a binary relation, we transform this
relation to n-ary relation. However this n-ary relation still has only one attribute and
Simple key.

6.2.1 The construction of information or data
Problem1 which is presented in 2.6 sets the following question:
How to recognize in formal way who or which procedure created the information.
Although there are the different tries to solve this problem, example 6.2 shows
that the binary relation in combination with knowledge-column can be powerful
solution for this problem. In 6.2 we have the construction where one information is
created by two sources.

Generally speaking the binary relation enables the construction of information.
So we don’t have a data, rather we have the construction of a data and associated

6.3 About some terms in this paper
(posted
December 4, 2007)
In this paper special attention is devoted to constructions which enable us to solve and
design the databases in which the attributes of the entities (or relationship) are changeable
or knowledge about the entities (or relationship) is changeable.
Basic constructions are entities (relationships) and states of entities (relationships).
An entity (relationship) has its states (an entity possesses states). Formally it can be said
that the identifier of the entity (or relationship) determines one set of its identifiers of state.
Of course the same identifier of an entity (relationship) corresponds to all its identifiers of
state.
The entity is defined by its attributes like in the E/R model. In literature the same term is in
used for both the real world entity and for the entity’s abstraction. Besides these two, I will
use the term entity also for abstract entities which don’t have the corresponding real world entities. It will be
always defined which form of the term is applied.

The identifier of an entity (relationship) can identify the following:
1) an entity in the real world or
2) an abstraction of the entity or
3) both, i.e. a real world entity and its abstraction
It is also possible that an entity doesn’t have an identifier of entity.

Database design determines which of these cases we will apply. Of course we should
be able to identify real world entities, abstractions or both. These three possibilities

7   The Semantic Model and Database Design

7.1.     Identifying the Plurality
In the process of identifying a plurality there are two constructions. I will first consider the
construction of the entities:

Construction1 (or first step)
(i)  We will construct an entity which is distinguishable from any other entity. To do this we
will use the corresponding entities attributes. If the entities attributes can’t establish the
unique entity then we will add to the entity a new attribute.  The new attribute will later
become an identifier of the entity. This construction is done first as an abstraction that is
represented by a scheme of the
corresponding entity set.
(ii) For more complex databases, instead of an entity we will use an entity’s state. The state
of an entity is uniquely determined by the entity’s attributes and by knowledge about the
entity attributes.

Constructuin2 (or second step)
Here we will construct identifiers.
Regarding Construction1:
(i) For each unique entity we will construct an identifier of the entity
(ii) For each unique state of the entity we will construct an identifier of the state of the entity.
--------------
Similar to the above is the construction of relationships.
Now we will define the following principles:

The Principle of Distinction
This is construction of the unique entity OR the construction of the unique state of the entity
as described in Construction1

Principle of Identification
This is the construction of the unique identifiers as described in Construction 2

Example:
During a phone call, we would never say the following: “May I speak with the 5 foot tall and
has blue eyes and has brown hair and …”
Rather, we will say: “May I speak with John?”

The aforementioned identifiers can exist in the real world and they are simultaneously the
identifiers of our abstraction. In real life we often make mistakes by not distinguishing between
the aforementioned two principles.
The state of an entity has two identifiers: the identifier of entity and the identifier of the state
of the entity.