Relationship. Relationship Variables
Independent variable. The researcher should strive to operate only on the independent variable in the experiment. An experiment where this condition is met is called pure experiment. But more often than not, during an experiment, by varying one variable, the experimenter also changes a number of others. This change can be caused by the action of the experimenter and is due to the relationship between two variables. For example, in an experiment on developing a simple motor skill, he punishes the subject for failures electric shock. The size of the punishment can act as an independent variable, and the speed of skill development can act as a dependent variable. Punishment not only reinforces the appropriate reactions in the subject, but also gives rise to situational anxiety in him, which affects the results - it increases the number of errors and reduces the speed of skill development.
The central problem in conducting experimental research is identifying the independent variable and isolating it from other variables. The independent variables in a psychological experiment can be:
characteristics of tasks;
·features of the situation (external conditions);
· controlled characteristics (states) of the subject.
The latter are often called “organism variables.” Sometimes isolated fourth type variables - constant characteristics subject (intelligence, gender, age, etc.), but, in my opinion, they belong to additional variables, since they cannot be influenced, but can only take into account their level when forming experimental and control groups.
The characteristics of the task are something that the experimenter can manipulate more or less freely. According to the tradition coming from behaviorism, it is believed that the experimenter varies only the characteristics of the stimuli (stimulus variables) but he has much more options at his disposal. The experimenter can vary the stimuli or task material, change the type of response of the subject (verbal or nonverbal response), change the rating scale, etc. He can vary the instructions, changing the goals that the subject must achieve during the task. The experimenter can vary the means that the subject has to solve the problem and put obstacles in front of him. He can change the system of rewards and punishments during the task, etc.
The features of the situation include those variables that are not directly included in the structure of the experimental task performed by the subject. This could be the temperature in the room, the environment, the presence of an external observer, etc.
Experiments to identify the effect of social facilitation (amplification) were carried out according to the following scheme: the subject was given any sensorimotor or intellectual task. He first performed it alone, and then in the presence of another person or several people (the sequence, of course, varied in different groups). The change in the productivity of the subjects was assessed. In this case, the subject’s task remained unchanged, only the external conditions of the experiment changed.
What can the experimenter vary?
Firstly, these are the physical parameters of the situation: the location of the equipment, appearance rooms, lighting, sounds and noises, temperature, placement of furniture, painting of walls, time of the experiment (time of day, duration, etc.). That is, all the physical parameters of the situation that are not stimuli.
Secondly, these are socio-psychological parameters: isolation - work in the presence of an experimenter, work alone - work with a group, etc.
Thirdly, these are the features of communication and interaction between the subject(s) and the experimenter.
Judging by publications in scientific journals, in recent years there has been a sharp increase in the number of experimental studies that use varying environmental conditions.
“Organismal variables,” or uncontrollable characteristics of the subjects, include physical, biological, psychological, socio-psychological and social characteristics. They are traditionally referred to as “variables,” although most are constant or relatively constant throughout life. The influence of differential psychological, demographic and other constant parameters on an individual’s behavior is studied in correlation studies. However, the authors of most textbooks on the theory of psychological method, for example M. Matlin, classify these parameters as independent variables of the experiment.
As a rule, in modern experimental research, the differential psychological characteristics of individuals, such as intelligence, gender, age, social position (status), etc., are taken into account as additional variables that are controlled by the experimenter in a general psychological experiment. But these variables can turn into a “second main variable” in differential psychological research, and then a factorial design is used.
Dependent variable. Psychologists deal with the behavior of the subject, so parameters of verbal and nonverbal behavior are selected as the dependent variable. These include: the number of mistakes the rat made while running the maze; the time the subject spent solving the problem, changes in his facial expressions when watching an erotic film; motor reaction time sound signal etc.
The choice of behavioral parameter is determined by the initial experimental hypothesis. The researcher must specify it as much as possible, i.e. ensure that the dependent variable is operationalized - amenable to registration during the experiment.
Behavior parameters can be divided into formal-dynamic and substantive. Formal-dynamic (or spatio-temporal) parameters are quite easy to record with hardware. Let's give examples of these parameters.
1. Accuracy. The most frequently recorded parameter. Since most of the tasks presented to the subject in psychological experiments are achievement tasks, accuracy or the opposite parameter - the error of actions - will be the main recorded parameter of behavior.
2. Latency. Mental processes occur hidden from the outside observer. The time from the moment the signal is presented to the choice of response is called latent time. In some cases, latent time is the most important characteristic of the process, for example, when solving mental problems.
3. Duration, or speed, execution. It is a characteristic of executive action. The time between the selection of an action and the end of its execution is called the speed of action (as opposed to latent time).
4. Pace, or frequency of actions. The most important characteristic, especially when studying the simplest forms of behavior.
5. Productivity. The ratio of the number of errors or the quality of execution of actions to the execution time. It serves as the most important characteristic in the study of learning, cognitive processes, decision-making processes, etc. Contentful parameters of behavior involve categorizing the form of behavior either in terms of ordinary language or in terms of the theory whose assumptions are tested in a given experiment.
Recognition various forms behavior is a matter for specially trained experts or observers. It takes considerable experience to characterize one act as a manifestation of submission, and another as a manifestation of servility.
The problem of recording qualitative features of behavior is solved through: a) training observers and developing observation cards; b) measuring formal dynamic characteristics of behavior using tests.
The dependent variable must be valid and reliable. The reliability of a variable is manifested in the stability of its recordability when experimental conditions change over time. The validity of a dependent variable is determined only under specific experimental conditions and in relation to a specific hypothesis.
Three types of dependent variables can be distinguished: 1) simultaneous; 2) multidimensional; 3) fundamental. In the first case, only one parameter is recorded, and it is this parameter that is considered to be a manifestation of the dependent variable (there is a functional relationship between them linear connection), as, for example, when studying the time of a simple sensorimotor reaction. In the second case, the dependent variable is multidimensional. For example, the level of intellectual productivity is manifested in the time it takes to solve a problem, its quality, and the difficulty of the problem solved. These parameters can be fixed independently. In the third case, when the relationship between the individual parameters of a multivariate dependent variable is known, the parameters are considered as arguments, and the dependent variable itself is considered as a function. For example, a fundamental measurement of the level of aggression F(a) is considered as a function of its individual manifestations (A) facial expressions, pantomimes, swearing, assault, etc.
F(a) =f(a 1,a 2,...,a n).
There is another important property of a dependent variable, namely, the sensitivity (sensitivity) of the dependent variable to changes in the independent one. The point is that manipulation of the independent variable affects the change in the dependent variable. If we manipulate the independent variable, but the dependent variable does not change, then the dependent variable is non-positive with respect to the independent one. Two variants of manifestation of non-positivity of the dependent variable are called “ceiling effect” and “floor effect”. The first case occurs when the task presented is so simple that the level of its implementation is much higher than all levels of the independent variable. The second effect, on the contrary, occurs when the task is so difficult that the level of its performance is below all levels of the independent variable.
So, like other components of psychological research, the dependent variable must be valid, reliable, and sensitive to changes in the level of the independent variable.
There are two main techniques for recording changes in the dependent variable. The first is used most often in experiments involving one subject. Changes in the dependent variable are recorded during the experiment following changes in the level of the independent variable. An example is the recording of results in learning experiments. The learning curve is a classic trend - changes in the success of completing tasks depending on the number of trials (time of the experiment). To process such data, the statistical apparatus of trend analysis is used. The second technique for recording changes in the level of an independent variable is called delayed measurement. A certain period of time passes between the impact and the effect; its duration is determined by the distance between the effect and the cause. For example, taking a dose of alcohol increases the time of the sensorimotor reaction not immediately, but after a certain time. The same can be said about the effect of memorizing a specific number of foreign words on the success of translating a text into a rare language: the effect does not appear immediately (if it does).
Relationships between variables. The construction of modern experimental psychology is based on K. Lewin’s formula - behavior is a function of personality and situation:
Neobehaviorists put in the formula instead R(personality) ABOUT(organism), which is more accurate if we consider not only people but also animals as test subjects, and the personality is reduced to the organism.
Be that as it may, most specialists in the theory of psychological experimentation, in particular McGuigan, believe that there are two types of laws in psychology: 1) “stimulus-response”; 2) “organism-behavior”.
The first type of laws is discovered during experimental research, when the stimulus (task, situation) is an independent variable, and the dependent variable is the response of the subject.
The second type of laws is a product of the method of systematic observation and measurement, since the properties of the body cannot be controlled by psychological means.
Are there "crossovers"? Of course. Indeed, in a psychological experiment, the influence of so-called additional variables is often taken into account, most of which are differential psychological characteristics. Therefore, it makes sense to add to the list "system" laws, describing the influence of a situation on the behavior of a person with certain properties. But in psychophysiological and psychopharmacological experiments it is possible to influence the state of the body, and in the course of a formative experiment - to purposefully and irreversibly change certain personality properties.
In a classic psychological behavioral experiment, a functional dependence of the form
Where R- the answer is a S- situation (stimulus, task). Variable S varies systematically, and the changes in the subject’s response determined by it are recorded. During the study, the conditions under which the subject behaves in one way or another are revealed. The result is recorded in the form of a linear or nonlinear relationship.
Another type of dependency is symbolized as the dependence of behavior on the personal properties or states of the subject’s body:
R = f (O) or R = f (P).
The dependence of the subject's behavior on one or another state of the body (illness, fatigue, level of activation, frustration of needs, etc.) or on personal characteristics (anxiety, motivation, etc.) is studied. Research is conducted with the participation of groups of people that differ in a given characteristic: property or current condition.
Naturally, these two strict dependencies are the simplest forms of relationships between variables. More complex dependencies established in a specific experiment are possible; in particular, factorial designs make it possible to identify dependencies of the form R = f(S 1, S 2), when the subject’s answer depends on two variable parameters of the situation, and behavior is a function of the state of the organism and the environment.
Let's focus on Levin's formula. In general form, it expresses the ideal of experimental psychology - the ability to predict the behavior of a specific individual in a certain situation. The variable “personality”, which is part of this formula, can hardly be considered only as “additional”. The neobehaviourist tradition suggests using the term “intervening” variable. IN Lately for such “variables” - personality traits and states - the term “moderator variable” was assigned, i.e. intermediary
Let's consider the main possible options for relationships between dependent variables. There are at least six types of variable relationships. The first, which is also the simplest, is the absence of dependence. Graphically, it is expressed in the form of a straight line parallel to the x-axis on the graph, where along the x-axis (X) levels of the independent variable are plotted. The dependent variable is not sensitive to changes in the independent variable (see Figure 4.8).
A monotonically increasing dependence is observed when an increase in the values of the independent variable corresponds to a change in the dependent variable (see Fig. 4.9).
A monotonically decreasing dependence is observed if an increase in the values of the independent variable corresponds to a decrease in the level of the independent variable (see Fig. 4.10).
Nonlinear dependence U-shaped type is found in most experiments in which features of mental regulation of behavior are revealed: (see Fig. 4.11).
Inverted U-shaped dependence is obtained in numerous experimental and correlational studies both in personality psychology, motivation, and in social psychology(see Fig. 4.12).
The last version of the dependence is not found as often as the previous ones - a complex quasiperiodic dependence of the level of the dependent variable on the level of the independent one (see Fig. 4.13).
When choosing a description method, the “principle of economy” applies. Any simple description is better than a complex description, even if they are equally successful. Therefore, arguments common in domestic scientific discussions like “Everything is much more complicated in reality than the author imagines” are, to say the least, meaningless. Moreover, no one knows how “in reality”.
The so-called “complex description”, “multidimensional description” is often simply an attempt to avoid solving a scientific problem, a way of disguising personal incompetence, which they want to hide behind a tangle of correlations and complex formulas where everything is equal to everything.
IN basis for constructing modern experimental psycho logic lies K. Levin's formula – behavior is a function of personality and situation:B =f(P; S).
The dependence of the subject’s behavior on a particular situation (stimulus, task), state of the body (illness, fatigue, level of activation, frustration of needs, etc.) or on personal properties (anxiety, motivation, etc.) is studied. Research is conducted with the participation of groups of people who differ in this characteristic.
Levin's formula in general form expresses ideal of experimental psychology: the ability to predict the behavior of a specific person in a certain situation. The “personality” variable, which is part of this formula, according to the tradition of neobehaviorism is called “ intermediate» variable or more modern "moderator variable", i.e. intermediary
Let's consider main possible relationship options between variables. There are five main types of variable relationships.
1. No dependence. Graphically, it is expressed in the form of a straight line parallel to the abscissa axis on a graph, where the levels of the independent variable are plotted along the abscissa (X) axis, and the levels of the dependent variable are plotted along the ordinate (Y) axis. The dependent variable is not sensitive to changes in the independent variable.
2. A monotonically increasing dependence is observed when an increase in the values of the independent variable corresponds to a change in the dependent variable.
Level of sensations
Sound intensity
3. A monotonically decreasing dependence is observed if an increase in the values of the independent variable corresponds to a decrease in the level of the dependent variable.
Number of plays
Time elapsed from the moment of memorization.
4. A nonlinear U-type dependence is found in most experiments in which Peculiarities of mental regulation of behavior are revealed:
Anxiety level
5. An inverted U-shaped relationship is obtained in numerous experimental and correlational studies, both in personality psychology, motivation, and social psychology.
Efficiency
joint
problem solving
p Group size
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Theoretical foundations of database organization. Relational data model.
(http://www.intuit.ru/department/database/rdbintro/)
Approaches to organizing databases
Hierarchical databases
This model is based on a hierarchical data model. In this model there is one main object and the rest are subordinate objects located at different levels of the hierarchy. Object relationships form a hierarchical tree with one root object.
A hierarchical database consists of an ordered collection of multiple instances of the same tree type. The integrity of links between ancestors and descendants is automatically maintained. Basic rule: no child can exist without its parent (see Fig. 1).
Rice. 1 Hierarchical data model diagram
A typical representative (the most famous and widespread) is the Information Management System (IMS) from IBM. The first version appeared in 1968. Many databases of this system are still supported
Network Databases
The network approach to data organization is an extension of the hierarchical one. In hierarchical structures, a child record must have exactly one ancestor; in a network data structure, a child can have any number of ancestors.
IN network model data, any object can be both a master and a slave at the same time, and can participate in the formation of any number of relationships with other objects. A network database consists of a set of records and a set of connections between these records, and more precisely, a set of instances of each type from a set of record types specified in the database schema and a set of instances of each type from a given set of connection types (see Fig. 2).
Rice. 2 Network model diagram
A typical representative is the Integrated Database Management System (IDMS) from Cullinet Software, Inc., designed for use on IBM mainstream machines running most operating systems. The system's architecture is based on proposals from the Data Base Task Group (DBTG) of the Committee on Programming Languages of the Conference on Data Systems Languages (CODASYL), the organization responsible for defining the COBOL programming language. The DBTG report was published in 1971, and later several systems emerged, including IDMS.
Relational Databases
It is generally accepted that the relational approach to database organization was founded in the late 1960s. Edgar Codd. In recent decades, this approach has been the most common (with the caveat that in what is commonly called relational database systems based on the SQL language, some important principles classical relational approach). The following properties are considered to be the advantages of the relational approach: the relational approach is based on a small number of intuitive abstractions, on the basis of which simple modeling of the most common subject areas is possible; these abstractions can be precisely and formally defined; the theoretical basis of the relational approach to organizing databases is the simple and powerful mathematical apparatus of set theory and mathematical logic; the relational approach provides the possibility of non-navigational data manipulation without the need to know the specific physical organization of databases in external memory. Computer World did not immediately recognize relational systems. In the 70s of the last century, when almost all the main theoretical results had already been obtained and even the first prototypes of relational DBMSs existed, many authoritative experts denied the possibility of achieving effective implementation of such systems. However, the advantages of the relational approach and the development of methods and algorithms for organizing and managing relational databases led to the fact that by the end of the 80s, relational systems took a dominant position in the global DBMS market.
The relational data model is based on mathematical principles stemming directly from set theory and predicate logic. These principles were first applied to the field of data modeling in the late 1960s. Dr. E.F. Codd, then working at IBM, and first published in the technical paper "A Relational Data Model for Large Shared Data Banks." This article is the founder of modern relational database theory. Dr. Codd identified 13 rules relational model(which are called Codd's 12 rules).
Codd's 12 Rules:
1. A relational DBMS must be able to fully manage the database through its relational capabilities.
2. Information rule - all information in a relational database (including table and column names) must be defined strictly as values in tables.
3. Guaranteed access - any value in a relational database must be guaranteed to be available for use through a combination of table name, primary key value and column name
4. Support for null values - The DBMS must be able to work with null values (unknown or unused values), as opposed to default values and independently for any domains.
5. Online relational catalog - a description of the database and its contents should be presented at a logical level as tables to which queries can be applied using the database language.
6. Comprehensive data management language - At least one of the supported languages must have a well-defined syntax and be comprehensive. It must support data structure description and manipulation, integrity rules, authorization and transactions.
7. Views update rule - all views that are theoretically updateable can be updated through the system.
8. Insertion, update and deletion - the DBMS supports not only the query for data selection, but also insertion, update and deletion
9. Physical independence of data - for application programs and special programs changes in physical data access methods and data storage structures are logically unaffected.
10. Logical data independence - application programs and special programs are not logically affected, within reason, by changes in table structures.
11. Integrity independence - the database language must be able to define integrity rules. They should be stored in the online directory and there should be no way to bypass them.
12. Independence of distribution - application programs and special programs are not logically affected by whether the data is used for the first time or reused.
13. Integrity - the inability to bypass integrity rules defined through the database language by using languages low level
Codd proposed the use of relational algebra in RDBMS to partition data into related sets. He organized his database system around a concept based on data sets.
Introduction to the relational data model
Basic concepts of the relational data model
Let us highlight the following basic concepts of relational databases: data type, domain, attribute, tuple, relation, primary key.
To begin with, let us show the meaning of these concepts using the example of the EMPLOYEES relation, which contains information about the employees of a certain enterprise (Fig. 3).
Rice. 3 Correlation of the basic concepts of the relational approach
Data type
Data values stored in relational database data are typed, i.e. the type of each stored value is known. The concept of a data type in the relational data model fully corresponds to the concept of a data type in programming languages. Recall that the traditional (lax) definition of a data type consists of three main components: the definition of a set of values of this type; defining a set of operations applicable to values of the type; determining the method of external representation of type values (literals).
Typically, modern relational databases allow the storage of character, numeric data (exact and approximate), specialized numeric data (such as “money”), as well as special “temporal” data (date, time, time interval). An approach to introducing user-defined capabilities into relational systems is actively developing. own types data.
In the example in Fig. 3 we deal with three types of data: character strings, integers and “money”.
Domain
The concept of a domain is more specific to databases, although there are analogies with subtypes in some programming languages. In general, a domain is determined by specifying some basic type the data to which the domain elements belong, and an arbitrary Boolean expression applied to the element of that data type (domain constraints).
A data element is a domain element if and only if the evaluation of this Boolean expression results in true (for Boolean values we will use the notation true and false or true and false interchangeably). Each domain is associated with a name that is unique among the names of all domains in the corresponding database.
The most correct intuitive interpretation of the concept of a domain is its perception as an admissible potential, limited subset of values of a given type. For example, the domain NAMES in our example is defined on the base type of character strings, but its values can only include those strings that can represent names (in particular, to be able to represent Russian names, such strings cannot begin with a soft or hard character and not may be longer, for example 20 characters). If a certain attribute of a relationship is defined on a certain domain (as, for example, in Fig. 3 the SLU_NAME attribute is defined on the NAMES domain), then the domain constraint subsequently plays the role of an integrity constraint imposed on the values of this attribute.
It should also be noted the semantic load of the domain concept: data are considered comparable only if they belong to the same domain. In our example, the values of the domains PASS NUMBER and DEPARTMENT NUMBER are of the type integer, but are not comparable (allowing them to be compared would be pointless).
Relation head, tuple, relation body, relation value, relation variable
The concept of a relation is the most fundamental in the relational approach to organizing databases, since the n-ary relation is the only generic structure of data stored in a relational database. This is reflected in the general name of the approach - the term relational derived from relation. However, the term relation itself is extremely imprecise, because when we talk about any data that is stored, we must mean the type of that data, the values of that type, and the variables in which the values are stored. Accordingly, to clarify the term relation, the concepts of relation header, relation value and relation variable are distinguished. In addition, we need the auxiliary concept of a tuple.
So, the header (or schema) of the relationship r (Hr) is a finite set of ordered pairs of the form
If all the attributes of the relation header are defined on different domains, then in order not to produce unnecessary names, it is reasonable to use the names of the corresponding domains to name the attributes (not forgetting, of course, that this is just a convenient way of naming that does not eliminate the differences between domain concepts and attribute).
By motorcade tr corresponding to the header Hr is the set of ordered triplets of the form
Meaning Vr of the relation r is called a pair of sets Hr and Br. One of the acceptable values of the EMPLOYEES relation is shown in Fig. 2.1.
114 Part I. Basic Concepts
3.5. OPTIMIZATION
As described in Section 3.2, all relational operations such as reduction, projection and join are performed on set level. This is why relational languages are often called non-procedural because the user specifies what to do rather than how to do it. In fact, the user only communicates what he needs, without specifying the procedure for obtaining the result. The process of navigation (moving) through the stored database in order to satisfy the user's request is performed automatically by the system, and not manually by the user. Therefore, relational systems are sometimes called systems automatic navigation. In non-relational systems, the user is primarily responsible for navigating the database. In Fig. Figure 3.5 provides a vivid illustration of the advantages of automatic navigation - the SQL INSERT statement is contrasted with manually prepared navigation code. To achieve the same result, such code would probably need to be prepared by a user of any non-relational system (in this case, the CODASYL network system; the example is taken from the chapter on network databases in ). It should be noted that the parts and supplier database is again used as an example here. Please refer to section 3.9 for details.
Despite the previous comments, it should be noted that non-procedural is, although a generally accepted, but not entirely accurate term, because procedural and non-procedural are relative concepts. Typically, all we can say with certainty is whether language A is more (or less) procedural than language B. So it would be more accurate to say that relational languages such as SQL are characterized by higher level of abstraction, than typical programming languages like C++ or COBOL (or the data sublanguages typically found in non-relational DBMSs; see Figure 3.5). In principle, it is the higher level of abstraction that contributes to the increased productivity of programmers that is typical for relational systems.
Responsibility for organizing the execution of automatic navigation is assigned to a very important component of the DBMS - the optimizer (we already mentioned it in Chapter 2). In other words, the optimizer's job is to choose the most efficient execution method for each user request. For example, let's say the user made the following request (using Tutorial D again).
(EMP WHERE EMP# = EMP# (“E4”)) ( SALARY )
Explanation. The expression in the first brackets (EMP WHERE ...) means that the operation of reducing the current value of the relation variable EMP is applied, concerning the row in which the value of the EMP# column is equal to E4. The language construct used here, which is the column name SALARY enclosed in curly braces, means that the result of the reduce operation is projected onto the SALARY column. The result of this projection operation is a one-column, one-row relation that contains the earnings of employee E4. (Note that this case makes implicit use of the relational property of closedness: we have written a nested expression that uses the result of the reduce operation as input to the projection operation.)
Rice. 3.5. Examples of automatic and manual navigation
Even in this simple example, there may be at least two ways to access the required data.
1. Sequentially physically scan the (stored version) of the EMP relation variable until the required record is found.
2. If there is an index on the column EMP# (in the stored version) of the relation variable (which probably does exist, since the column is unique, and most systems actually require an index to be created to ensure uniqueness), then navigating through that index directly to employee number E4's data.
The optimizer will determine which of two possible strategies to apply. In general, to implement any given relational query, the optimizer will select a strategy based on considerations such as the following:
116 Part I. Basic Concepts
■ which relation variables are referenced in the query;
■ how large these variable ratios are currently;
■ what indices exist;
■ how selective are these indices;
■ how data is physically grouped on the disk;
■ what relational operations are used; etc.
Therefore, we repeat: the user indicates in the request what data he needs, and not how to get it, while the data access strategy is selected by the optimizer (automatic navigation). As a result, users and user programs become independent of the access strategies used, which, of course, is absolutely necessary if we want to achieve real independence from the physical representation of data.
For more information about the optimizer, see Chapter 18.
3.6. CATALOG
As noted in Chapter 2, every DBMS must support catalog or dictionary functions. The directory is usually located where various schemas (external, conceptual, internal) and everything related to mappings ("external-conceptual", "conceptual-internal", "external-external") are stored. In other words, the catalog contains detailed information (sometimes called descriptive information or metadata) concerning various objects that are relevant to the system itself. Examples of such objects include relation variables, indexes, integrity constraints, security constraints, etc. Descriptive information is necessary to ensure the correct operation of the system. For example, the optimizer uses directory information about indexes and other physical storage structures, as well as other information it needs to decide how to fulfill a given user request (see Chapter 18). Likewise, the security engine uses directory information about users and security restrictions (Chapter 17) to allow or deny an incoming request.
A remarkable property of relational systems is that they the directory also consists of relation variables(more precisely, from the system variables of the relationship, on-
so named to distinguish them from ordinary user ones). As a result, the user can access the directory in the same way as their data. For example, the catalog of any SQL system usually contains system relation variables TABLES and COLUMNS, the purpose of which is to describe the tables (that is, relation variables) known to the system and the columns of these tables. For a department and employee database, the relationship variables4 TABLES and COLUMNS can be schematically represented in a hierarchical structure as shown in Fig. 3.6.
4 Note that based on the presence of the ROWCOUNT column in this figure, we can conclude that performing INSERT and DELETE operations on the database will require updating the catalog data as a side effect. In practice, the ROWCOUNT column is usually updated only on special request (for example, when running a utility), so the values of this column will not always be up to date.
Rice. 3.6. Directory of departments and employees database (shown schematically)
Note. As mentioned in Chapter 2, a directory must also describe itself, i.e. include entries describing variable relations of the directory itself (see Exercise 3.3).
Now suppose that a user of a departments and employees database wanted to know which columns the relation variable DEPT contained (assuming, of course, that for some reason the user did not have this information). Then the required expression will look like this.
(COLUMNS WHERE TABNAME = "DEPT") ( COLNAME )
Here's another example. Suppose you need to find out which relation variables contain the EMP# column.
(COLUMNS WHERE COLNAME = "EMP#") ( TABNAME )
Self-test exercise. What will be the result of executing the following expression?
((TABLES JOIN COLUMNS)
WHERE COLLECTION< 5) { TABNAME, COLNAME }
3.7. BASIC RELATIONSHIP AND REPRESENTATION VARIABLES
We have already seen that, based on the relational values assigned to a set of relational variables like DEPT and EMP, relational expressions allow one to obtain many other relational values, for example by joining two relational variables. Now we need to introduce a few more new terms. The initial (specified) relationship variables are called basic relation variables, and the values assigned to them are called basic relations. A relation that is obtained or can be obtained from a base relation as a result of executing some relational expressions is called a derived relation.
118 Part I. Basic concepts
Note. The basic relation variables are called real relation variables.
Relational systems obviously must provide a means for creating basic relational variables in the first place. In SQL, for example, this function is provided by the CREATE TABLE statement (here the word TABLE is used in the narrow sense, as a basic relation variable). The underlying relationship variables must, of course, be named, as shown below.
CREATE TABLE EMP ... ;
However, relational systems usually support another kind of named relation variables called representations. IN at any given moment their meaning is a derived relation (and therefore, simplistically, we can consider that representation is derived relation variable). The value of a given representation at a given time is the result of the evaluation of a certain relational expression at that moment, and said relational expression is determined at the time that representation is created. For example, you can use the following statement to define the TOPEMP representation.
CREATE VIEW TOPEM AS
(EMP WHERE SALARY > 3 3K
) (EMP#, ENAME, SALARY) ;
Note. Since this is not important at the moment, the example uses a mixed notation of SQL and Tutorial D for convenience.
When this statement is executed, the expression following the AS keyword is actually defining representation is not calculated, but is simply remembered by the system (usually by saving it in a directory under the specified name TOPEMP). However, from the user's point of view, everything looks as if a very real relation variable named TOPEMP appeared in the database, having the current value, which is shown in Fig. 3.7 only in unshaded areas. And the user must be able to operate on this representation exactly as if it were a regular underlying relation variable.
Rice. 3.7. Virtual relation variable TOREMP (unshaded areas) as a representation of the basic relation variable EMP
Note. It was already said above that if such relation variables as DEPT and EMP can be considered real, then the relation variable TOPEMP should be considered as a virtual relation variable, in other words, as a relation variable that externally exists as such, but in fact it does not (the meaning of this relation variable at any given moment depends on the values of some
other relation variables). Indeed, in representations they are called
virtual relation variables.
Be careful, however, that by noting that the value of the relation variable TOPEMP is the relation that would be the result if the expression defining the representation were actually evaluated, we do not mean to say that there is a separate copy of that data. In other words, we do not mean that the expression defining the view is actually evaluated. Instead, the view is essentially just a window through which you can see part of the value of the underlying EMP relation variable. It follows that any changes to the underlying relation variable will automatically and immediately appear in such a window (of course, if these changes relate to the unshaded part of the real relation variable). Likewise, changes made to the relation variable TOPEMP will be automatically and immediately applied to the real relation variable EMP and will therefore be visible through this window (examples will be given later).
Below is an example of a query using the TOPEMP representation.
(TOREMP WHERE SALARY< 42К) { ЕМР#, SALARY }
If the data in Fig. 3.7, then the result will have the form shown in Fig. 3.8.
Rice. 3.8. Result of using the TOPEMP representation
Conceptually, view operations like the one discussed above are similar to lookup operations, which are actually implemented by replacing a reference to the view name with an expression that defines the view (that is, an expression stored in a directory). Therefore, in the example considered, the original expression
(TOREMP WHERE SALARY< 42К) { ЕМР#, SALARY }
modified by the system as follows.
(((EMP WHERE SALARY > ZZK) (EMP#, ENAME, SALARY)) WHERE SALARY< 42К) { ЕМР#, SALARY }
Here italicized is the name of the view in the original expression and the replacement text in the modified version. After a certain number of rearrangements, this expression can be simplified (Chapter 18) and represented as follows.
(EMP WHERE SALARY > ZZK AND SALARY< 42К) { ЕМР#, SALARY }
Evaluating this expression produces the result shown above. In other words, the original operation on the representation is simply converted to an equivalent operation on the corresponding underlying relation variable, and then
120 Part I. Basic concepts
the resulting equivalent operation is performed in the usual way (more precisely, it is optimized and executed in the usual way).
As another example, consider the DELETE operation.
DELETE TOPEMP WHERE SALARY< 42K ;
In fact, the following operation will be performed.
DELETE EMP WHERE SALARY > ZZK AND SALARY< 42К;
The TOPEMP representation discussed here is a very simple one, consisting (informally speaking) of a subset of rows and columns of a single underlying relation variable. However, in principle, the definition of a view can have arbitrary difficulty(it may even refer to other views). For example, the following is a view whose definition involves concatenating two basic relation variables.
CREATE VIEW JOINEX AS
((EMP JOIN DEPT) WHERE BUDGET > 7M) ( EMP#, DEPT# ) ;
We will return to the issue of defining and processing views in Chapter 10. By the way, it is now possible to explain the meaning of the remark given at the end of Section 2.2 regarding the fact that the term view in a relational context has a rather specific meaning that does not coincide with the meaning assigned to it in the ANSI/SPARC architecture. At the external level of this architecture, the database is perceived as external presentation, defined by an external schema (and different users may have different external views). In relational systems, on the contrary, the representation, as explained above, is specifically named derivative of a virtual relation variable. Therefore, the relational analogue external representation
An ANSI/SPARC definition is typically a set of several relation variables, each of which is a representation in a relational sense. An external schema consists of definitions of such representations. (It follows that in the relational model, views are one of the ways to provide logical independence from data, although once again it should be noted that modern commercial products have serious shortcomings in this area. See Chapter 10 for details.)
The ANSI/SPARC architecture is quite general and allows arbitrary transformations between the external and conceptual levels. In principle, even the types of data structures supported at these two levels may be different: for example, the conceptual level may be relational, while an external representation of a hierarchical type may be conveyed to a particular user5. However, in practice, most systems use the same types of structures as base structures at both levels. Relational products are no exception to this general rule—the view is still a relation variable, just like the underlying relation variables. And because the same object types are supported at both levels, the same data sublanguage (usually SQL) is used at both levels. Indeed, the fact that a view is a variable
5 An example of this possibility is given in Chapter 27.
relations is as important to relational systems as it is to mathematics that a subset is a set.
Note. However, documentation for actual SQL products and the SQL language standard itself often seems to ignore this nuance (Chapter 4), since it is common to see references to “tables and views” (i.e., implying that a view is not a table). We advise you to avoid this common mistake and use term tables (or variable relations) only to denote the base tables (or basic relation variables).
There is another issue worth considering regarding basic attitude variables and beliefs. The difference between a basic relation variable and a representation is often characterized as follows.
■ Basic relationship variables "really exist" in the sense that they embody data that is actually stored in the database.
■ Views, on the other hand, don't "really exist" but simply provide different ways of viewing "real" data.
However, such a characterization, although useful in an informal sense, does not accurately reflect the true state of affairs. Indeed, users may treat basic relation variables as physically stored, since in fact the main purpose of creating relational systems is to enable the user to work with basic relation variables as if they were physically present, without worrying about how those relation variables are physically represented in memory . But (and this is a very significant “but”), such user views on how data is processed cannot be interpreted as if the base relation variable is directly physically stored relation variable (for example, as a single stored file). As explained in Section 3.2, basic relation variables are best thought of as an abstraction for some set of stored data—an abstraction that hides all the details of the data storage layer. In principle, the underlying relation variable and its stored equivalent6 can vary to an arbitrary degree.
A simple example will help clarify this question. Let's look at the database of departments and employees again. In most modern relational systems it would probably be implemented as two stored files, one for each database relation variable. But there is absolutely no argument against creating one stored file of hierarchically stored records, each of which consists, firstly, of the department number, title and budget for some department, and, secondly, along with them are given the employee's personnel number, last name and the salary of each employee working in this department. In other words, any suitable method can be used to physically store data (see Appendix A for more information), but at the logical level the data should always look the same.
6 The following quote from a recent book demonstrates some of the misunderstandings discussed here, as well as those discussed in section 3.3: “It is important to distinguish between stored relationships, which are tables, and virtual relationships, which are ideas...[We] will only use the term relationship in cases where the term "table" or "view" could be used instead. If it becomes necessary to emphasize that a given relation is a stored relation and not a representation, then in this case we will use the term basic relation or base table." Such quotes, unfortunately, are not uncommon.
Relationship. Variable relationships. Meaning of relation variables. Basic relation variables and their representations. Predicates and propositions
Computer science, cybernetics and programming
Relationship. Variable relationships. Meaning of relation variables. Basic relation variables and their representations.
Relationship. Variable relationships. Meaning of relation variables. Basic relation variables and their representations. Predicates and statements.
Definitions
n -ary relation R, or R power ratio n , called a subset of the Cartesian product of sets D 1, D 2, D 3... Dn (n >=1), not necessarily different. Source sets D 1, D 2, D 3...are called domains in the model (in the DBMS the concept of data type is used).
The relation has a simple graphical interpretation; it can be represented as a table, the columns (fields, attributes) of which correspond to occurrences of domains in the relation, and the rows (records) to sets of values taken from the source domains. The number of rows (tuples) is called the cardinal number of the relation (cardinality), or the cardinality of the relation.
This table has a number of properties:
- There are no two identical rows in the table.
- The table has columns corresponding to the attributes of the relationship.
- Each attribute in a relationship has a unique name.
- The order of rows in the table is arbitrary.
An attribute here refers to the occurrence of a domain in a relation. The rows of a relation are called tuples.
The header Hr (or schema) of the relation r a finite set of ordered pairs of the form
Tuple tr corresponding to header Hr set of ordered triplets of the form
The body Br of the relation is an unordered set of distinct tuples tr.
The value Vr of a relation r is a pair of sets Hr and Br.
The concept of a primary key is also useful - this is a set of attributes that uniquely defines a tuple and is minimal among all its subsets (that is, none of the attributes can be removed). When adding new records, the primary key must remain the primary key (for example, it would be incorrect to use the set First Name + Patronymic + Last Name of an employee as the primary key, even if at the time the table was created there were no full namesakes among the people entered in it).
Basic concepts:
An object a domain element that can be clearly identified.
The properties of an object are displayed using variables, which are elementary units of information within the database, and are called attributes.
Attribute/field/columna logically indivisible element related to the properties of some object or process.
Attributes are divided into attribute attributes and basis attributes.
- Attributes signsare a qualitative characteristic of the object.
- Attributes basecharacterize the quantitative side of the object.
Attributes have many valid values.
The set of all possible values of an attribute is called domain.
The set of attributes characterizing one object is calledrecord/tuple/string.
The record type is determined by the properties of the object.
Key an attribute or a set of attributes that uniquely define an object.
Potential Keya key that can identify an object.
From the set of potential keys, one primary key is selected. Otherkeys alternative.
Surrogate keyan attribute that is created to uniquely identify an object.
Secondary key an attribute that assigns an object to a certain group.
Table indexingthe process of creating an index file, which describes how to sort a table by a selected field or expression.
In modern DBMSs, several indexes can be stored in one index file.
A filter can be applied to the table.
Filter logical condition that allows you to display only those records that are satisfactory. this condition.
In the database noun. concept representation virtual table , which can display data from one or more tables.
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