Quasi-Functional Relations in Logic and Other Fields of Knowledge

Classical science was mainly focused on the investigation of the cause-effect relations between phenomena obeying the principle of determinism: a certain phenomenon under certain conditions causes a certain effect. These relationships are expressible via functions. A function can be understood as an operation that, when applied to a certain object from the function domain, obtains a certain object from the function range. In nature, society, and cognition, there are relations of a different type. They obey the principle of quasi-determinism: one of several phenomena under one of several conditions causes one of several consequences. These relations are expressed by means of quasi-functions. In the article, a quasi-function is understood as an operation that is applied to an object from a subset of the (now) quasi-function definition domain to obtain an object from a subset of the quasi-function range. Since subsets of the domains of definitions and values of a quasi-function can consist of a single object, a special case of a quasi-function is a function. A special case of a quasi-function is also complete uncertainty (randomness) if the subsets from which the objects are selected coincide with the domain and range of the quasi-function. Since the function can be probabilistic, multi-valued, etc., then the quasifunction can be the same. The article reviews the main results of research on the application of the principle of quasi-functionality (quasi-determinism, limited determinism, nondeterminism) in the field of logic, mathematics, epistemology, natural science, technical and social knowledge. The methods of constructing quasi-functional logics of aletic ontological and logical modalities, and deontic logic are given. Ontological aletic modal logics are based on quasi-matrices, and logical ones are based on the semantics of restricted sets of state descriptions. Since methods of constructing logical systems that express relations in forms between judgments containing logical modalities are less known than systems with ontological modalities, they are given more space. Some problems for further research of quasifunctional logic and the methodological role of the principle of quasi-determinism in scientific knowledge are formulated, for example, the task of constructing logical systems, statements in which contain both logical and ontological modalities. It is proposed to apply the principle of quasifunctionality in the development of management decisions, etc.

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