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Design+ Modern interpretations of probability

introduce infinite-valued logic and can be formulated as the categories of subjective probability. The concept of
probabilistic conclusions. Specifically, if a is the probability subjective probability has significant applications in
of realization of some event, then the probability of not modern decision-making theory. Secondly, what is the
realizing the same event will be defined as (1-a); if a and place of subjective probability among other interpretations of
b are probabilities of realizing some two events, then the probability? Some scientists consider subjective probability
probability of joint (simultaneous) realization of these two the only possible one, the basis of all other interpretations.
events will not exceed the value min (a, b), the probability However, if one accepts such an interpretation of probability
of realizing at least one of the two events will not exceed as the only true and admissible one, one cannot rationally
the value min (a, b), and the probability of realizing at least explain the existence of the stability of frequencies of
one of the two events will not exceed the value min (a, b). mass phenomena, which is the basis for the introduction
of an objective (empirical) interpretation of probability.
The connection between the concepts of probability
and logic is clearly shown if we interpret the probability Besides, based on the concept of subjective probability, one
cannot explain the successful practical applications of the
of the realization of an event as a measure of confidence concept of statistical probability in various fields of human
in such realization. In this interpretation, the probability activities, including forecasting procedures.
of realization of an event is considered as a measure of
the subject’s belief in this realization, that is, the fact of 9. Probabilistic logic
realization of the event is “put” into the logic of thinking
of the subject, who, of course, in his conclusions relies Probabilistic logic is a section of logic that studies logical
on the relevant available knowledge, or his intuition and structures for which the set of truth components of
experience. An event, in the realization of which there statements consists not of two values: “true” and “false,”
is no full belief but with some assumptions about the as in binary logic, but of all real numbers placed on
possibility of such realization (the possibility of realization the interval [0, 1]. In this case, as in binary logic, zero
is not rejected completely), is considered probable; the corresponds to an impossible event, and one to an event
value of the specified probability characterizes its truth. that occurs reliably. Truth values in probabilistic logic
Given that the probability value in this interpretation relies are called truth probabilities, degrees of likelihood, or
18,19
on the degree of belief of the subject, this interpretation of degrees of confirmation. Probabilities are added to the
probability is called subjective probability. system of binary logic as a new relation connecting the
set of statements (variables) and the set of truth values of
In an explicitly developed form, the English scientist these statements (the set of values of the corresponding
Frank Ramsey first presented such an interpretation of functions) from the interval 0 ≤ P(A) ≤ 1, where P (A)
probability in his book Fundamentals of Mathematics, is the probability of the truth of the statement (event,
published in 1920. The interpretation of probability as a variable) A. Probabilistic logic is often considered a
measure of confidence is convenient because it directly refinement of inductive logic because the relationship
indicates the practical method of calculating probability. between the premises of an inductive judgment can be
To realize this method, Ramsey offered the analysis evaluated using a probability, the value of which can be
of the betting process by some subjects regarding the determined numerically or by comparing the probability
realization of event A. If, in the process of betting, the of the truth of a statement (event, variable). Today, the
subject estimates the probability of the realization of event importance of probabilistic logic in scientific research
A based on appropriate knowledge, logic, experience, and and practical activities is continuously growing due to the
intuition, to the highest bet, then this bet is offered by significant development of information systems, artificial
this subject. For example, if the bet 3:2 was accepted, the neural networks, and robotics.
subject estimates the probability of the realization of event One of the varieties of probabilistic logic systems is
A as 3/5. Although this method has disadvantages, it has systems of pragmatic probabilistic logic, in which probability
become a foundation for further development in building is applied to analyze pragmatic aspects of research. Such
probabilistic conclusions.
logical systems include the probabilistic logic of action,
The interpretation of probability as a measure of probabilistic logic of choice, probabilistic logic of change,
confidence, that is, introducing the concept of subjective probabilistic logic of decision-making, probabilistic logic
probability, raises at least two questions. Firstly, can the of preference, probabilistic logic of attractiveness, and
concept of subjective probability be applied in a practical probabilistic logic of priority. In some of these systems, the
activity? Today, this question has a quite concrete answer: concept of probability does not appear explicitly, but its
wherever there is a need for a pragmatic assessment of connection with the basic concepts of the corresponding
the realization of some event, we inevitably encounter structure in each case is traceable. 18,20 If the realization

Volume 2 Issue 2 (2025) 13 doi: 10.36922/dp.6387