THE FORMALIZED MATHEMATICAL CONTENT COGNITIVE MANAGEMENT
Abstract
Problem of the formalized mathematical content management for any given subject domain is considered. The content represented by domain ontology as the unified variety of elementary knowledge classes and relations for such classes as subject domain content. The ontology includes variety different types of entities and relations between them analogous to categories and structures of mathematical language. Such knowledge is formal that allows developing correct algorithms for the tasks’ solution searching processes at abstract and applied knowledge domains based on ontologies. The content management consists in modeling the processes of realization the cognitive goals adapted to the professional activity domain. The considered system of cognitive goals classes based on the weakly formalized cognitive goals hierarchy of classes introduced by B. Blum's and corresponding cognitive operations realized as result of the thinking processes versatile analysis. The cognitive goal realization makes algebraic structures for the complex semantic representations synthesized by application of ontology elements. Simulating the synthesis processes defined by regular structures of abstract knowledge processing operations extracted from hierarchy of such operations classes, analogous of fundamental types of morphisms at fundamental mathematical systems. Achieving the exact definitions in work realized at this work by narrowing the formal goals interpretation for considered system of Blum’s cognitive goals classification. The independence of goals and operations based on applying the different classes of objects as goals and operations domains and ranges, different classes of mathematical operations and scenarios of simulating the cognitive goals realization processes. The resulted table of mathematical associations for B. Blum goals classification includes information about integrated mathematical specifications and abstract knowledge processing operations for knowledge representation formalisms, added by domains and ranges for such operations. Formal descriptions provided for regular formats of knowledge neighborhoods and series, examples of scenarios for formal operations combinations that realize the cognitive goals of understanding and estimation made by special language constructs.
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