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problems of improving the global security system. The leaders of the countries of Central Asia, correctly aware of the extremely important importance of these processes, discuss security issues and other pressing issues on a regular basis bilaterally and within the framework of the CACO (Central Asian Cooperation Organization). Joint decisions are being developed and are making important contributions to ensuring security in the region.
Used sources:
1.Islam Karimov. Uzbekistan: national independence, economy, politics, ideology. Tashkent: Uzbekistan, 1996. T. 1.
2.Islam Karimov. Ideology is the uniting flag of a nation, society, state. Answers to the questions of the editor-in-chief of the journal "Tafakkur". Tashkent: Uzbekistan, 1999.
УДК 345
Sattarov A.M.
Сатаров А.М. Andijan state medical Institute Андижанский государственный медицинский институт Theacher of the department of social and humanitarian sciences Преподаватель кафедры «Социальный-гуманитарный науки»
Uzbekistan, the city of Andijan Узбекистан, город Андижан THE ESSENCE OF MODAL LOGIC Abstract: In this article, we discuss modal logic, probabilistic logic, modal logistics
Keywords: logic, modal logic., Traditional or classical logic
СУЩНОСТЬ МОДАЛЬНОЙ ЛОГИКИ Аннотация: В данным статье обсуждать модальная логика, вероятностная логика, модальная логистика
Ключевые слова: логика, модальная логика., традиционная или классическая логика
Traditional or classical logic, which we have considered so far, is the simplest and most common logical system. It proceeds from the fact that the atomic (simple) judgments and concepts from which reasoning is based and which are no longer analyzed, or truths, or false, but neither one nor the other. However, many concepts and judgments of everyday and scientific reasoning do not fit so well into categories of true and false.
The true meaning of the proposition «Probably tomorrow will rain» is very, very undetermined. Some logicians, beginning with Aristotle, began to take into account the difference between truths that are such, so to speak, by necessity, and by random truths. So there was a modal logic and probabilistic logic.Unlike classical logic, attributing judgments and concepts to two truth values: truth and falsehood, modal logic operates with truth values such as «possible», «necessary», «impossible», etc. The first attempt to build a modal logic was undertaken by
Aristotle in his essay «The First and Second Analysts»(chapters third and eighth -twenty-second «first analysts» are devoted to it).
Fowever, as noted by I. Lukosevich (1878-1956), the Aristotelian exposition of modal logic was not free from shortcomings. The pupil of Aristotle, Theophrastus (370-288 BC), clarified Aristotle's doctrine of the modality of judgments. Medieval scholastics developed Aristotelian modal syllogistics. Modern research in the field of modal logic is characterized by the desire to build axiomatic systems of modal logic. The most famous of them are the systems of Lewis, Ackerman and Lukasevich.Modal and probabilistic logic are rather specific branches of logic. Acquaintance with their fundamentals is necessary for understanding the methodology of scientific research.
The modality of judgments is understood as the difference between judgment depending on whether they express a necessary or probabilistic (accidental) connection between the subject and the predicate. By modality judgments are divided into three groups: judgments of possibility (problematic), judgments of reality (assertorial) and judgments of necessity (apodictic). In the judgment of the possibility, the possibility of the presence or absence of the attributes of the object, referred to in this judgment, is displayed. His formula «S is probably (not) P». This will be, for example, the opinion «Perhaps in Kiev in April this year there will be snow.» In the judgment of reality, the presence or absence of a feature is ascertained. His formula «S is (is not) P». The judgment «Kyiv is on the Dnieper» is a statement of reality. In the judgment of necessity, a sign is displayed that is (there is no) in the object under all conditions. His formula «S is necessary (there is no) P». An example of the judgment of necessity may be the following statement: «The body, without support, falls to Earth. »
The judgments of possibility, reality and necessity are divided by quality into affirmative and negative, and also by quantity into private and general.A meaningful typology of modalities is constructed depending on which factors are responsible for the modality (the term «modality» means conditional on something).
His formula «S is probably (not) P». This will be, for example, the opinion «Perhaps in Kiev in April this year there will be snow.» In the judgment of reality, the presence or absence of a feature is ascertained. His formula «S is (is not) P». The judgment «Kyiv is on the Dnieper» is a statement of reality. In the judgment of necessity, a sign is displayed that is (there is no) in the object under all conditions. His formula «S is necessary (there is no) P». An example of the judgment of necessity may be the following statement: «The body, without support, falls to Earth.»
A meaningful typology of modalities is constructed depending on which factors are responsible for the modality (the term «modality» means conditional on something).In modal logic, logical and physical modalities are distinguished. Logical modalities are the laws of logic and mathematics. The number of physical or causal (causal) modalities includes all laws of experimental sciences. Thus, the
proposition «It is not true that P and not P», «2 + 2 = 4», etc. Express logical modalities, and the judgments «PV = RT», «U = IR», and so on. - Physical.
Absolute and relative modalities are also distinguished. Absolute modalities include the laws of logic, mathematics, and other sciences necessary in themselves, independent of anything. Let's say, judgments «A = A», «2 + 3 = 5», «S = Vt», etc. Relative modalities are such, necessary or not necessary, dependent on something.Such modalities will be, for example, judgments: «A rectangle is a square if its sides are equal», «Water boils at 1000 C at atmospheric pressure of 760 mm Hg», etc.
Logical and physical modalities, whether absolute or relative, are combined into aleutvic modalities. Modalities that characterize permissible (or unacceptable) actions of people are called deontological. They are expressed in judgments that use such words (modal operators) as «necessary», «allowed», «forbidden», «have the right», etc. Examples of such modalities will be judgments: «In Ukraine, the propaganda of war is prohibited,» «Citizens of Ukraine have the right to profess any religion or none, be atheists», etc. Deontological modalities are the subject of study of such sciences as ethics, jurisprudence.
The modalities that characterize the evidence of any judgments are called epistemological. In judgments of epistemological modality, words (modal operators) are used, as «provable», «refutable». Examples of such modalities may be judgments: «It is proved that there is life on Mars», «It is refutable that light has a wave nature», etc.Epistemological modalities in their properties are close to the alevtic modalities, and the operator is «provable», the operator «is necessary», the operator is «refutable» - the operator is «impossible». Finally, there is sometimes a distinction between the modality of de dicto («about speech») relating to judgment as a whole and de re («about a thing») that relate to the predicate. Thus, the proposition «It is possible that there is life on Mars» will be a de dicto judgment, and the proposition «On Mars is possible life» - de re. However, in most modern systems of modal logic, modalities are interpreted as «absolute» logical modalities de dicto.
Used sources: 1.Андреев Д. Роза мира. - М., 1992. С. 244. 2.Омар Хайям. Рубаи. - Т., 1981. С. 111
Э.Фарходжонова Н. Ф. Влияние идеологических процессов на национальную идею в условиях глобализации // Мир науки и образования. - 2016. - №. 2 (6).4. Мирзахолов Х. Т., Абдурахмонова Б. Р. Самосовершенствование личности-цель эстетического воспитания // Молодой ученый. - 2016. - №. 4. -с. 720-722.
