The paper proposes some applications the automated synthesis of tableau calculi in intelligent web-based education systems (WBES). We propose architecture of an intelligent webbased education system that use automated synthesis of tableau calculi. Current solutions mostly use only one deduction system for target logic. In case of the semantic web ecosystem it is description logics (DLs) deduction system based on tableau or hyper-tableau. This paper also examines some disadvantages of using the automated synthesis tableau calculi in WBES. We analyze how to use the method in an intelligent analysis of student’s solutions. Keywords—Automated synthesis, Tableau calculi, Technology enhanced learning, Web-based education systems.