Формальная модель мультимодального образовательного графа знаний для интеллектуальных обучающих систем
Аннотация
В статье представлена формальная модель мультимодального образовательного графа знаний (MEKG), предназначенного для структурированного представления знаний в интеллектуальных обучающих системах. Предложена математическая модель MEKG = ⟨E,R, A,M,T,F⟩, интегрирующая гетерогенные сущности (концепции, навыки, учебные материалы, задания), типизированные отношения (предшествования, вхождения, оценивания), мультимодальные атрибуты и темпоральную динамику. Определены формальные свойства модели: ацикличность отношений предшествования, полнота покрытия компетенций, согласованность мультимодальных представлений. Разработаны алгоритмы верификации целостности графа и механизмы версионирования. Проведён сравнительный анализ с существующими подходами, включая отечественные работы по инженерии знаний. Экспериментальная оценка на образовательном курсе по программированию (215 концепций, 312 связей предшествования) подтвердила применимость модели для автоматизации диагностики знаний и персонализации обучения: интеграция с системой трассировки знаний повысила точность прогнозирования (AUC) на 2,5 процентных пункта.
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