Modeling and formalization. Modeling and formalization presentation for a lesson in informatics and ICT (grade 11) on the topic Presentation modeling and formalization

You can choose: Modeling as a method of scientific knowledge. Model. Modeling as a method of scientific knowledge. Model. Model classification Material models. Information models. Formalization of models. Systematic approach to modeling Statistical and dynamic models. Graphical information models. Tabular models. Hierarchical models. Network information models. Object information models.

Modeling as a method of scientific knowledge. Model. Modeling as a method of scientific knowledge. Model. Model: - this is some simplified semblance of a real object, phenomenon or process; is a material or mentally imagined object that replaces the original object with the aim of studying it, while retaining some typical features and properties of the original that are important for this research.

Content The model is necessary in order to: The model is necessary in order to: learn how to manage an object or process and determine the best management methods for given goals and criteria (optimization); predict the direct and indirect consequences of the implementation of the specified methods and forms of impact on the object, process. to understand how a specific object is arranged, what are its structure, basic properties, laws of development and interaction with the outside world;

Main stages of modeling Main stages of modeling Stage I. Problem statement Problem description Purpose of modeling Object analysis Stage II. Model development Information model Sign model Computer model III stage. Computer experiment stage IV. Analysis of simulation results Results are in line with the goal Results do not meet the goal Contents

Information models. Information models. Information models represent objects and processes in a figurative or symbolic form. Figurative models (drawings, photographs, etc.) are visual images of objects fixed on any medium (paper, photographic and film) Sign information models are built using different languages (sign systems). Sign information can be presented in the form of text (for example, a program in a programming language), a formula (for example, Newton's second law F = m * a), tables (for example, the periodic table of elements of D.I.Mendeleev), etc.

Throughout its history, humanity has used various methods and tools to create information models. These methods have been constantly improved. So, the first information models were created in the form of rock paintings, but now information models are usually built and studied using modern computer technologies. Contents Information models.

Formalization of models. Formalization of models. Natural and formal languages are used to represent information models in one form or another. Natural languages are used to create descriptive information models. Formal information models (mathematical, logical, etc.) are built with the help of formal languages. One of the most widely used formal languages is mathematics. The language of mathematics is a collection of formal languages. You will get acquainted with some of them (algebra, geometry, trigonometry) at school, with others (set theory, probability theory, etc.) you will be able to familiarize yourself in the process of further education.

The language of algebra allows one to formalize functional relationships between quantities. Thus, Newton formalized the heliocentric system of the world by discovering the laws of mechanics and the law of universal gravitation and writing them down in the form of algebraic functional dependencies. In the school physics course, many different functional dependencies are considered, expressed in the language of algebra, which are mathematical models of the studied phenomena or processes. The language of logic algebra (propositional algebra) allows one to build formal logical models. With the help of propositional algebra, it is possible to formalize (write in the form of logical expressions) simple and complex propositions expressed in natural language. Building logical models allows you to solve logical problems, build logical models of computer devices (adder, trigger), and so on. Formalization of models. Formalization of models.

The process of building information models using formal languages is called formalization. In the process of cognizing the surrounding world, humanity constantly uses modeling and formalization. When studying a new object, first, its descriptive information model is usually built in a natural language, then it is formalized, that is, expressed using formal languages (mathematics, logic, etc.). Contents Formalization of models. Formalization of models.

Systematic approach to modeling. Systematic approach to modeling. The concept of the system. The world around us consists of many different objects, each of which has various properties, and at the same time the objects interact with each other. For example, the planets of our solar system have different properties (mass, geometric dimensions, etc.) and, according to the law of universal gravitation, interact with the sun and with each other. The planets are part of a larger object - the solar system, and the solar system is part of our of the Milky Way galaxy. On the other hand, planets are made up of atoms of various chemical elements, and atoms are made up of elementary particles. Thus, we can conclude that almost every object consists of other objects, that is, it is a system. Content A system is a whole consisting of interconnected objects, which are called system elements. For example, a computer is a system consisting of various devices, while the devices are interconnected both hardware (physically connected to each other) and functionally (information is exchanged between devices.An important feature of the system is its integral functioning.

System analysis To describe a system, it is not enough just to list its elements. It is necessary to indicate how these elements relate to each other. It is the presence of connections that turns a set of elements into a system. When you describe the elements of the system and indicate their interrelationships, thereby you will conduct a system analysis. Systematization Systematization is the process of turning a set of objects into a system. Systematization is of great importance. In everyday life, each of us is engaged in systematization - separates clothes for winter and summer, dishes into glasses, plates, pots. The systematization of knowledge in various sciences is invaluable. System analysis. Systematization System analysis. Systematization

Static information models At each moment of time, the system is in a certain state, which is characterized by the composition of the elements, the values of their properties, the magnitude and nature of the interaction between the elements, and so on. So, the state of the solar system at any time is characterized by the composition of the objects included in it (the sun, planets, etc.), their properties (size, position in space, etc.), the magnitude and nature of interaction with each other (gravitational forces, using electromagnetic waves, etc.). Models describing the state of the system at a certain point in time are called static information models. In physics, an example of static information models are models that describe simple mechanisms, in biology, models of the structure of plants and animals, in chemistry, models of the structure of molecules and crystal lattices, and so on. Static and dynamic models Static and dynamic models

Dynamic information models The state of systems changes over time, that is, there are processes of change and development of systems. So, the planets move, their position changes relative to the Sun and each other; The sun, like any other star, develops, its chemical composition, radiation and so on change. Models describing the processes of change and development of systems are called dynamic information models. In physics, dynamic information models describe the movement of bodies, in biology - the development of organisms or animal populations, in chemistry - the processes of chemical reactions, and so on. Static and dynamic models Static and dynamic models

Static information model "Price of individual computer devices" Static information model "Price of individual computer devices" 5 Mouse 10 Keyboard 25 Case 50 CD-ROM drive x32 30 Sound card 16 bit 200 Monitor 15 30 Video card 4 MB 150 Hard disk 4 GB 20 Disk drive 3.5 30 Memory 16 MB 200 (Pentium II processor 200 350 MHz) 100 System board Price (in USD) Device name

Dynamic information model "Change in the price of a computer" Dynamic information model "Change in the price of a computer" Price of a Pentium II computer Years Contents

Graphical information models. Graphical information models. Graphic information models are the simplest type of models that convey the external features of an object: size, shape, color. Graphic models are more informative than verbal ones. Graphic models are: Maps - without maps it is difficult to imagine botany and biology, geography, military affairs, shipping, etc .; Drawings of technical devices, buildings; Electrical and radio circuits - physics, radio electronics; Graphs and diagrams (visual form of presenting numerical information)

Tabular models. Tabular models. Another common form of information model presentation is a rectangular table, consisting of rows and columns. In a tabular information model, objects or their properties are presented as a list, and their values are located in the cells of a rectangular table. Both static and dynamic information models can be expressed with tables. statically dynamic With the help of tables, information models are built in various subject areas. The presentation of mathematical functions, statistical data, timetables of trains, planes and lessons, etc. is widely known. Information presented in the form of tables is very convenient and easy to understand. Basic Table Concepts Basic Table Concepts How to format a table How to format a table What types are tables divided into? What types are tables divided into?

The table can reflect some process taking place over time. In mathematics, a rectangular table made up of numbers is called a matrix. If a matrix contains only zeros and ones, then it is called a binary matrix. The tables, which are binary matrices, reflect the qualitative nature of the relationship between objects (there is a road, no road; visiting does not visit, etc.). Matrix binary matrix Contents Tabular models. Tabular models. Complete the practice assignments

An example of a matrix. An example of a matrix. Pupil RussianAlgebraChemistryPhysicsHistoryMusic Alikin Petr Botov Ivan Volkov Ilya Galkina Nina Achievement

An example of a binary matrix. An example of a binary matrix. Pupil RussianAlgebraChemistryPhysicsHistoryMusic Alikin Petr Botov Ivan Volkov Ilya Galkina Nina Studied subjects The unit indicates the studied subject, and the unexplored subject is marked with zero.

Hierarchical information models. Hierarchical information models. We are surrounded by many different objects, each of which has certain properties. However, some groups of objects have the same general properties that distinguish them from objects in other groups. A group of objects that share the same general properties is called an object class. Within a class of objects, subclasses can be allocated, the objects of which have some special properties, in turn, subclasses can be divided into even smaller groups, and so on. This process of organizing objects is called the classification process.

Hierarchical information models. Hierarchical information models. In the process of classifying objects, information models are often built that have a hierarchical structure. In biology, the entire animal world is considered as a hierarchical system (type, class, order, family, genus, species), in computer science, a hierarchical file system is used, and so on. In a hierarchical information model, objects are categorized by level, from the first (top) level to the bottom (last) level. Each higher-level item can be composed of lower-level items, and a lower-level item can be a member of only one higher-level item.

Static hierarchical model. Consider the process of building an information hierarchical model in the form of a graph, which allows you to classify modern computers. The class Computers can be divided into three subclasses: Supercomputers, Supercomputers, Servers and Personal computers. Hierarchical information models. Hierarchical information models.

In the considered hierarchical model that classifies computers, there are three levels. The first, top, level contains the Computers element, it includes three elements of the second level Supercomputers, Servers and Personal computers. The latter includes three elements of the third, lower, level Desktop, Laptop and Pocket computers. The subclass Personal computers is divided, in turn, into Desktop, Laptop and Pocket computers.

The graph is a convenient way to visualize the structure of information models. The vertices of the graph (ovals) represent the elements of the system. Links between elements are shown on the graph with lines. If the line is directed (i.e. with an arrow), then it is called an arc. If there is no arrow, then this is an edge. Two vertices connected by an edge or arc are called adjacent. Relationships that are valid in both directions are called symmetric. Symmetric connections on the graph are edges. Graphs in this case are called undirected. Graphs in which the connections between objects are asymmetric (displayed by arcs) are called oriented. Hierarchical graphs are sometimes called trees. Information models on graphs. Information models on graphs. Complete the practice assignments

Flowcharts are another example of a directed graph. The flowchart of the algorithm is a graph of the control process for a certain performer. The blocks of the vertices of this graph designate individual commands that are given to the executor, and the arcs indicate the sequence of transitions from one command to another. Geometric figures that are used to indicate the vertices are as follows: -beginning and end of the sequence of actions - - initial data and result - -Actions - --condition (a question that can be answered only "Yes" or "No") Information models on graphs. Information models on graphs. Complete the practice assignments

Dynamic hierarchical model. To describe the historical process of changing generations of a family, dynamic information models in the form of a family tree are used. As an example, we can consider a fragment (X-XI centuries) of the family tree of the Rurik dynasty. A fragment (X-XI century) of the family tree of the Rurik dynasty. Information models on graphs. Information models on graphs. Dynamic hierarchical model ". Dynamic hierarchical model ".

Network information models. Many-to-many relationship. Network information models. Many-to-many relationship. Network information models are used to reflect systems with a complex structure, in which the links between elements are arbitrary. For example, various regional parts of the global computer network Internet (see figure) (American, European, Russian, Australian, and so on) are interconnected by high-speed communication lines. At the same time, some parts (for example, the American part) have direct connections with all regional parts of the Internet, while others can exchange information with each other only through the American part (for example, the Russian and Australian). Contents Let's build a graph that reflects the structure of the global Internet. The nodes of the graph are regional networks. The connections between the vertices are of a two-sided nature and therefore are depicted by undirected lines (edges), and the graph itself is therefore called undirected

Object information models. Object information models. Now let's look at another approach to information modeling, which is called the object-oriented approach. The main concept here is "object". An object is a part of the reality around us. From the point of view of human perception, objects can be divided into the following groups: tangible or visible objects (for example: a chair, a car, a bridge); images created by thinking (for example: poem, piece of music, mathematical theorem). The information model of an object should reflect a certain set of its properties. Object properties Object properties are a collection of features that distinguish it from other objects.

Examples of objects and their properties. Examples of objects and their properties. Object name Properties My teacher Name, Work experience, Course read My hard disk Size, Amount of used memory Important document Name, Date of creation Amount of occupied memory, Location

Objects with the same properties and behavior form an object class. Every object is an instance of some class. An instance of a class (object) is a specific object or image, and a class defines a set of objects with the same properties and behavior. A class can generate an arbitrary number of objects, but any object belongs to a strictly fixed class. Content

Goals:

give students a general idea of the formalization of the object;

to form the concept of formalization;

develop the research competence of students in the formalization of the model, logical thinking, broaden their horizons;

develop cognitive interest, educate information culture.

Didactic software

Computer type IBM, Windows operating system, MS Office XP and higher,

Presentation Formalization . pps .

Theoretical material

Formalization as the most important stage of modeling

Slide number 1

In his activity - artistic, scientific, practical - a person very often creates some image of that object (process or phenomenon) with which he has to or will have to deal - a model of this object. The creation of this image always pursues a certain goal. The model is not important in itself, but as a tool that facilitates learning or visualization.

In the process of learning about the world around us and communicating, we are faced with formalization at almost every step: we formulate thoughts, draw up reports, fill out all kinds of forms and forms, transform formulas. When studying a new object, first, its descriptive information model is usually built in a natural language, then it is formalized, that is, it is expressed using formal languages (mathematics, logic, etc.).

Thus, before building a model of an object (phenomenon, process), it is necessary to single out its constituent elements and connections between them (conduct a system analysis) and "translate" (display) the resulting structure into some predetermined form - formalize information.

Slide number 2

Formalization is the process of highlighting and translating the internal structure of an object, phenomenon or process into a specific information structure - a form. Modeling any system is impossible without preliminary formalization. In fact, formalization is the first and very important step in the modeling process.

Formalization is the replacement of a real object or process with its formal description, that is, its information model.

Slide number 3

Having built an information model, a person uses it instead of the original object to study the properties of this object, predict its behavior, etc. Before building a complex structure, for example, a bridge, designers make its drawings, perform strength calculations, allowable loads. Thus, instead of a real bridge, they deal with its model description in the form of drawings, mathematical formulas. If the designers wish to reproduce the bridge in a reduced size, then it will already be a full-scale model - a model of the bridge.

Slide number 4

Natural languages are used to create descriptive information models. Numerous descriptive information models are known in the history of science; for example, Copernicus' heliocentric model of the world was formulated as follows:

The earth revolves around its axis and around the sun;

the orbits of all planets pass around the sun.

Slide number 5

Formal languages are used to construct formal information models(mathematical, logical, etc.). One of the most widely used formal languages is mathematics. Models built using mathematical concepts and formulas are called mathematical models. The language of mathematics is a collection of formal languages.

Slides number 6-8

The language of algebra (algebra of statements) allows one to formalize functional relationships between quantities. Thus, Newton formalized the heliocentric system of the world by discovering the laws of mechanics and the law of universal gravitation and writing them down in the form of algebraic functional dependencies. In the school physics course, many different functional dependencies are considered, expressed in the language of algebra, which are mathematical models of the studied phenomena or processes.

The language of logic algebra allows you to build formal logical models. With the help of propositional algebra, it is possible to formalize (write in the form of logical expressions) simple and complex propositions expressed in natural language. Building logical models allows you to solve logical problems, build logical models of computer devices (adder, trigger), and so on.

The encyclopedic dictionary provides the following interpretation of this concept: “ Formalization- This is the presentation and study of any meaningful area of knowledge (scientific theory, reasoning, search procedures, etc.) in the form of a formal system or calculus.

Slide number 9

In the context of modeling under formalization we will understand the process of translating the description of the problem in general form (the general formulation of the problem) into the language of formal representation in order to create a computer model and study it. From the point of view of information processing, it is necessary to define the initial data (what needs to be processed) and describe the processing rules (how to process).

Slide number 10

Formalization is one of the main tools of mathematics. Because mathematics operates with really non-existent entities, abstract concepts, describes laws, theorems, rules, hypotheses and so on, then it is impossible to do without agreements on the representation of all this.

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Slide captions:

Modeling and formalization Performed by the teacher of informatics MBOU secondary school No. 108 Samara Gazizova Ekaterina Aleksandrovna

Models and modeling One of the methods of cognition of objects of the surrounding world is modeling, which consists in creating and researching simplified substitutes for real objects. The replacement object is usually called the model, and the original object is called the prototype or original.

Models and modeling Modeling is used when the object under investigation is too large (solar system) or too small (atom), when the process proceeds very quickly (fuel processing in an internal combustion engine) or very slowly (geological processes), when the study of the object may turn out to be dangerous for others (atomic explosion), lead to its destruction (checking the seismic properties of a high-rise building) or when the creation of a real object is very expensive (new architectural solution), etc.

Stages of building an information model Analysis highlights the properties formalization Formalization is the replacement of a real object with its formal description, that is, its information model.

Types of models Model Full-scale (material) Information Descriptions of the original object in information coding languages Real objects, in a reduced or enlarged form, reproducing the appearance, structure or behavior of the object of modeling

Classification of information models

Figurative models Figurative models are visual images of objects fixed on some kind of information carrier.

Sign models Sign information models are built using different languages (sign systems). program lab; var a, b, s, p: integer; begin write ("Enter the length:"); readln (a); write ("Enter the width:"); readln (b); s: = a * b; p: = 2 * (a + b); writeln ("The area is equal to:", s); writeln ("Perimeter is:", p); end. Take care of our language, our beautiful Russian language is a treasure, this is an asset passed on to us by our predecessors! I.S. Turgenev

Mixed models Mixed information models use figurative and symbolic elements at the same time.

Verbal information models Verbal models are descriptions of objects, phenomena, events, processes in natural languages. For example, the heliocentric model of the world, which was proposed by Copernicus, was verbally described as follows: - The earth rotates around its axis and around the sun; - the orbits of all planets pass around the Sun. Many verbal models are contained in your school textbooks: a history textbook presents models of historical events, a geography textbook presents models of geographic objects and natural processes, and a biology textbook presents models of objects of the animal and plant world.

Mathematical models Information models built using mathematical concepts and formulas are called mathematical models. Using the language of algebra of logic, logical models are built - simple and complex statements expressed in natural language are formalized (written in the form of logical expressions). By constructing logical models, it is possible to solve logical problems, create logical models of devices, etc. Computer mathematical models At present, the most complex mathematical models can be implemented on a computer. In this case, such tools are used as: - programming systems; - spreadsheets; - specialized mathematical packages and software for modeling. Simulation is an artificial experiment in which, instead of carrying out field tests with real equipment, experiments are carried out using computer models.

Graphic information models A drawing is a conditional graphic image of an object with an exact ratio of its dimensions, obtained by the projection method. Diagram is a graphical representation that gives a visual representation of the ratio of any quantities or several values of the same quantity, of the change in their values. A graph is a line that gives a visual representation of the nature of the dependence of one quantity. A diagram is a representation of an object in general, main features using symbols. With the help of diagrams, both the appearance of an object and its structure can be represented.

"Properties of the object" - The ability of fabrics to change their color depending on the state. ... Fully or partially electrically conductive structure of the Object. New functions of the Object. New features of the Object. 5. A.V. Kislov, A.B. Ilyichev, I.A. Novikov. Measurement of tissue impedance.

"Model Object" - Conclusion. Specifications. Automatic construction of links between objects and replacement of formal neighbors with actual ones. Simple use of the METIS format for such a description. Counting based on the "working set" of objects. Account results, performance evaluation. There are no standards for a fairly wide class of cases.

"Stages of modeling" - Stage III Computer experiment. Stage II. Computer experiment. Stage IV. Stage II Development of the model. Description of the task. The purpose of the simulation. Model development. Stage III. Stages of modeling. Stage 1 problem statement. Stage I. Information model. Analysis of simulation results. Computer model.

"Modeling and formalization" - Interaction. Wednesday. Types of models: 1.subject-object-entity. Compliance (similarity). Limited growth model. Types of models: 2.subject-object- degree of formalization. Verbal description. Appearance. (Systems and data structures). Formalized. Target. OBJECT of modeling. Partially formalized.

"Types of information models" - Graphical models. Drawing. ToC. Examples of graphic information models: Graph of temperature changes. An example of an object-property table. Time. Graph. Schedule. ?. An example of an object-to-object table. Diagram. Tabular models. Mathematical models. Map. Verbal models. Scheme. Types of information models.

Model Development Steps - Descriptive information models are usually built using natural languages and pictures. Stage 3. Stage 5. Building a descriptive information model. The main stages of development and research of models on a computer. Practical task. Stage 1. Solar system model. Stage 4. Stage 2.

There are 18 presentations in total

Modeling and Formalization

Modeling

Modeling- a method of cognition, consisting in the creation and study of models.

Those. research of objects by building and studying models

Model concept

Model –

Model saves the most important characteristics and properties of the original.

The model "copies" the real object.

Model - any analogue, image (mental or conventional: an image, description, diagram, symbol, formula, drawing, graph, plan, map, table, etc.) of any object of research.

The same object can have many models , a different objects can be described one model .

Examples of models

The model is necessary in order to:

understand how arranged a real object: what is its structure, basic properties, laws of development and interaction with the outside world;
teach to rule object or process: determine the best management methods for given goals and criteria ( optimization);
predict direct or indirect consequences of the implementation of the specified methods and forms of impact on the object.

Model presentation forms

Model classes

Subject (material)- reproduce geometric, physical and other properties of objects in material form (globe, anatomical dummies, building models, etc.)

Information- represent objects and processes in figurative and iconic form

Classification of models by area of use

Instructional Models - used in training

Scientific and technical - created for the study of processes and phenomena

Experienced - these are reduced or enlarged copies of the designed object. Used to research and predict its future performance

Gaming - rehearsal of the object's behavior in various conditions

Imitation - reflection of reality to one degree or another (this is a trial and error method)

Formalization

Formalization – the process of building information models using formal languages.

Formal information models (mathematical, physical, logical, etc.) are built with the help of formal languages.

physical

information

1 question

Option 1

Option 2

A) subject model

B) information model

2 question

What class does the model in the figure belong to?

Option 1

Option 2

A) subject model

B) information model

A) information model

B) subject model

3 question

Option 1

some simplified semblance of a real object, which reflects the essential features (properties) of the studied real object, phenomenon or process

Option 2

A) model

B) modeling

C) formalization

A) formalization

B) modeling

B) model

4 question

Definitions are given, choose the correct answer

Option 1

Option 2

some simplified semblance of a real object, which reflects the essential features (properties) of the studied real object, phenomenon or process

A) formalization

B) modeling

A) model

B) modeling

B) model

C) formalization

5 question

Definitions are given, choose the correct answer

Option 1

Option 2

a cognitive method of creating and exploring models

the process of building information models using formal languages

A) formalization

B) modeling

A) model

B) modeling

B) model

C) formalization

6 question

Option 1

Option 2

A) figurative models

B) mixed models

A) mixed models

B) figurative models

C) iconic models

Question 7

The pictures show information models, what form do they refer to?

Option 1

Option 2

A) figurative models

B) mixed models

A) mixed models

B) figurative models

C) iconic models

8 question

Insert the missing word

Option 1

One and the same object can have many models, and different objects can be described by ………… .. by a model

Option 2

A) set

One and the same object can have …………… models, and different objects can be described by one model

A) set

Answers:

Option 1

Option 2

Question number

Correct answer

Rating scale

grade

Number of correct answers

Systematic approach to modeling

System concept

System is a collection of interconnected objects called system elements.

An important feature of the system is its holistic functioning.

The state of the system is characterized by its structure , that is, the composition and properties of elements, their relationships and connections among themselves.

Classification of models by the factor of time:

Dynamic- models describing the processes of change and development of the system

Static- models describing the state of the system at a certain point in time (the growth of class students on the day of the study)

Discrete (the growth of class students in 10 years, algorithms)

Continuous (measurement of atmospheric pressure during the day)

Types of information models

Tabular

Hierarchical

Network

Tabular information models

In a tabular information model, a list of objects or properties of the same type is placed in the first column (or row) of the table, and the values of their properties are placed in the following columns (or rows) of the table.