SOFTWARE ARCHITECTURE FOR MATHEMATICAL MODELING BASED ON INTERVAL AND ONTOLOGICAL APPROACH - MELNYK, Andriy (Herald of Khmelnytskyi National University. Technical sciences, 2022)
Mathematical knowledge is a term often used to describe various components of mathematical science, such as theorems, lemmas, axioms, proofs, etc.. By the term “knowledge from mathematical modeling” we understand the definition of a huge amount of knowledge, which is formalized both within the framework of a specific mathematical model and in the process of its construction, as well as related procedures of practical use. Compared to other forms of knowledge, such as rules, solution trees, mathematical knowledge is more abstract and more structured. In general, the ontological approach to mathematical modeling refers to the use of ontology, as it is based on the terms of mathematical modeling and descriptions of relationships between the main processes of its course.. The general ontological approach to mathematical modeling from an applied point of view does not allow to manage the processes of building mathematical models, because it can only be used to describe the area of mathematical modeling. From an applied point of view, most basic forms of mathematical knowledge are either embedded in specific software tools, such as models of aggregate operation in simulation software, or must be formally interpreted into a more general mathematical tool, following appropriate syntactic rules. Most of this type of knowledge relates to specific modeling tasks and is clearly implemented with the help of appropriate procedural descriptions, rather than declarative representations, unlike the philosophical vision of mathematical modeling. The paper substantiates the use of the ontological approach as an effective tool for managing the processes of building mathematical models based on interval data and using these models for applied problems. The use of the ontological model made it possible to formalize the process of obtaining, storing and using knowledge obtained in the process of mathematical modeling. The article also presents the features of building a software architecture for mathematical modeling based on interval analysis and an ontological approach. The technology for creating software based on the developed ontological add-on for mathematical modeling using interval data for various objects, as well as various forms of user interface implementation, is described. A number of diagrams illustrating the peculiarities of using the ontological approach based on interval data are presented and the peculiarities of its interpretation in applied fields, in particular, in the tasks of environmental monitoring, are described.