Abstract
The paper centers on building the semantics of the modal metatheory for studying the classes of algorithmic complexity. Further the effectiveness of this calculus is studied on the example of researching the famous problem of computational complexity theory – the question of equality of the classes P and NP. The new theoretical and methodological approach to the problem is provided. The original semantics was developed that can be used for description of relations between classes of algorithmic complexity from the complexity theory. On the basis of this semantics the complete calculus of the logic of the computational complexity can be developed in future. It is the first time when modal logic is used for studying the relations between classes of algorithmic complexity. New theoretical and methodological approaches to the classical problems of the complexity theory are proposed. Paper matters for computer science, philosophy of mathematics, logic and theory of algorithms, cryptography.
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