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Design+ Modern interpretations of probability

particularly noteworthy: processing the results of research, the available knowledge (available information) about the
measurements, and control of parameters of various objects, phenomena, and processes under study.
objects by nature (both in engineering practice and in Logical probability relies on the available body of
other areas of human activity), calculations of reliability knowledge (available information) and does not depend
indicators of technical objects (although, mainly predicted on unknown facts. In contrast, frequency probability relies
reliability at the design stage), analyzing the reliability of on facts existing in the real world of relationships of these
technical objects (although, mainly predicted reliability or those events and has no relation to the available body of
at the design stage), analyzing the reliability of technical knowledge.
objects, and analyzing the results of the analysis of the
reliability of technical objects. Today, methods that rely on structural-logical
schemes of such objects are widespread in the practice
At the same time, it should be clearly understood of calculations of fail-safety, analysis of emergencies, and
that probability theory and mathematical statistics construction of algorithms for diagnosing structurally
algorithms will only work if the primary information on complex technical objects. In this case, all signals available
the analyzed event is sufficient and if additional conditions in the object (in the broad meaning of the word, i.e.,
for implementing relevant studies are met. After all, these outpourings and reactions of different origins, such as
algorithms aim to process mass phenomena and arrays of electrical, mechanical, and hydraulic) are supplied by
information. Additionally, they have limitations in the form binary logical variables. The technical state of the object
of appropriate conditions that ensure the stability of the results is identified by the corresponding logical function that
of calculations, but they can neither be strictly proved nor actualizes the study and development of the concept of
tested in practice. If the available information is limited, logical probability and methods of logical-probabilistic
the events under study are not sufficiently numerous, the calculus, based on this concept. 26,27
uniformity of the conditions for the realization of these
events in the process of observation is not ensured, or In realizing the life cycle of any technical object, we
there are methodological difficulties with the calculations often have to face a situation when the available data
of probability indicators and the corresponding confidence are insufficient for applying probability theory methods
intervals – especially, when the value of these intervals is and algorithms associated with logical interpretations of
too large – then the results obtained may fail to reflect probabilities. One key task is establishing and aligning the
reality accurately. Under such conditions, searching for nomenclature and quality standards between the executor
other methods and algorithms to solve the set tasks is and the customer for the object proposed for development.
necessary. This involves considering and comparing various potential
scenarios for the future realization of the specified object
The interpenetration of the categories of logic and based on the generalized quality indicator. In addition,
probability opens up a space for logical interpretations it includes forecasting the “residual” levels of reliability
of probabilistic concepts and actualizes, and justifies the and safety indicators during the object’s operation, an
possibility of determining the prior value of probability especially critical task for long-term-use objects. The main
through the study of the space of possibilities. At the same advantage of such methods is the possibility of obtaining
time, such possibilities can be defined as unequal, with an adequate answer to the posed questions concerning
different weights. the analyzed object, process, or event in the presence of
Probabilistic logic is logic whose subject matter limited, incomplete, and inaccurate prior information,
is probabilistic variables (statements, hypotheses, which presented in numerical and non-numerical forms.
and judgments), regardless of whether probability is Notably, the amount of information sufficient for the initial
considered as a property of an individual variable (under idea about the properties of the analyzed structures can
such conditions, probability is attributed to a given be obtained based on expert evaluations (providing the
variable as an intermediate value between truth and experts with sufficient comfort regarding the formulation
falsity, i.e., within the range from zero to one) or as an of conclusions), comparison of prototypes, experience, and
evaluation of the relation of “ordinary” binary variables. intuition of specialists engaged in solving the set tasks.
Unlike in probability theory, labeling probability by
an exact number (defining probability by a particular 13. Conclusion
quantity) is not a major requirement in probabilistic logic. Probability theory is deeply and comprehensively
The logical apparatus built on such a basis is used for the developed. Despite certain methodological difficulties
approximate evaluation of hypotheses not by correlating regarding the compliance of the real data set in the research
them with reality, but through other categories that reflect space with the basic provisions, the probability theory

Volume 2 Issue 2 (2025) 17 doi: 10.36922/dp.6387