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The purpose of this paper is to establish the nature of mathematical modeling of systems within the framework of the object-semantic methodology.

The initial methodological position of the object-semantic approach is the principle of constructing concepts of informatics proceeding from fundamental categories and laws. As the appropriate foundation, this paper accepts the system-physical meta-ontology is being developed in this paper.

The genesis of system modeling is considered in the aspect of the evolution of language tools in the direction of objectification. A new conception of formalized knowledge is being put forward as the mathematical form of fixing time-invariant relations of the universe, reflecting regularity of the dynamics of natural or anthropogenic organization. Object knowledge is considered as a key component of the mathematical model, and the solving of system information problems with its use is characterized as “work of knowledge.” The establishment of the meta-ontological essence of modern mathematical modeling allows us to formulate its fundamental limitations.

The establishment of system-physical limitations of modern mathematical modeling outlines the boundaries from which it is necessary to proceed in the development of future paradigms of cognition of the surrounding world, which presuppose convergence, synthesis of causal (physicalism) and target (elevationism) determination.

The purpose of this paper is to investige the general computing mechanisms of solving the system information problems of interpretation and its fundamental limitations, due to physical basis Turing machine.

For creation of theoretical base of methodology, the authors make an attempt to demonstrate the possibility of a constructive building of Turing machine as meta-ontological basis of computing. In the course of this building the role of the operator of atomic implicative transition if-then as generic operator of recognition/decision-making is shown. In order to substantiate the thesis about the determinative role of implicative transition in the interpretation mechanisms, the authors will carry out the comparative analysis methods of interpretation in systems of pattern recognition and expert systems interpretation type.

The carried-out analysis allows to formulate a common mechanism underlying the classical methods of solving problems of interpretation and to concretize the fundamental limitations of these methods, caused computational basis of their actualization. The cybernetic interpretation of this mechanism is offered.

The fundamental limitations of classical methods of solving problems of interpretation sets the boundaries of the cybernetic approach and allows to outline a way out beyond it. In this context, the authors put forward knowledge-based mechanism of perceptual modeling of dynamics of system visual environment – autonomous agent.