Knowledge system: hierarchy of axioms, models and their verification

The article explores the possibilities for improving the system of knowledge, which currently lacks the necessary integrity, exists simultaneously in several contradictory paradigms, and is described in alternative, mutually untranslatable languages of various sciences and fields of knowledge. The possibilities for enhancing the system of knowledge can be realized through the systematization and generalization of knowledge in the form of a hierarchical structure, based on the involvement of several methodological levels, which include: the formation of a hierarchy of axioms; the establishment of formal theories of subject areas based on the chosen axiomatics and the uniform rules accepted within the framework of the current scientific paradigm; the determination of methodological approaches to the synthesis of formal models; topological verification of knowledge for ensuring the continuity of mappings and preserving consistency during the development and transformation of the entire system of knowledge as well as local systems of knowledge related to its fragments or manifestations. The research methodology is based on an evolutionary approach to cognition, according to which relatively large subject areas correspond to evolutionary levels of the universe, for which axiomatics is defined. The construction of a formal model is carried out using a special synthesis methodology. To justify the choice of a formal model, an original classification of models is proposed based on a wide range of criteria. The scientific novelty of the study lies in: the definition of a methodology for building a hierarchy of axioms; the establishment of three criteria for selecting the best axioms (evolutionarity, obviousness, and paradigmaticity); the identification of mechanisms for the emergence of incompleteness and contradictions in knowledge systems arising from the encapsulation of generalized knowledge of previous evolutionary levels, associated with information loss, as well as the determination of approaches to eliminating incompleteness and contradictions; the formalization of a special synthesis methodology for formal models, which includes accumulated synthesis experience, consolidated in the form of secondary laws of objects related to modeling, and the tools for describing the sequence of synthesis based on its linguistic interpretation; the formation of a comprehensive approach to solving the problem of formal models when they change beyond systemic determinacy. In the long term, the development of the knowledge system aims to define methodological approaches to the task of constructing linguistic forms for the translation of meanings between various subject areas while preserving continuity or redefining the meanings of knowledge.

knowledge system, hierarchy, axioms, evolution, subject area, universe, formal system, theory, model, verification