Non-finite methods of Reconstructions of Non-Classical Propositional Logic Variants based on the Theory of Structures in Control Problems of Complex Systems

The report explores the problem of developing a common base of mathematical support for the problem of modeling control systems for objects of great complexity. The problem of reconstructing variants of propositional logic based on structures whose elements are considered as truth values of formulas of reconstructed variants of propositional logic is considered. The reconstruction is based on the assumption that there is a homomorphism from the algebra of logic to the algebra of truth values. In the proposed version of the semantic approach to the classification of formal logical calculus as a result of the interaction of various logical moments, this interaction takes the form of an interconnection of algebraic structures on which the values of “judgments” take values, different types of measures on these structures and equivalence relations associated with them.