Using the scenario of an Automated Tutoring System 3.1 Develop a set of axioms for an automated tutoring system with a specific focus on teaching mathematical concepts. Explain the logical foundations and assumptions that underlie each axiom. Consider the essential principles that should govern interactions between the tutoring system and students. (10) 3.2 Explore the translation of the proposed axioms into predicate logic to formalize the relationships and constraints within the automated tutoring system. Provide a detailed step-by-step breakdown of how each axiom is expressed using predicates and quantifiers. Discuss the significance of this logical representation in guiding the system's decision-making processes. (10) 3.3 Establish a set of criteria for evaluating the effectiveness of the axiomatic system. Consider factors such as consistency (absence of contradiction), completeness (coverage of relevant scenarios), and clarity (ease of understanding). Discuss the importance of these criteria in ensuring the reliability and usability of the tutoring system. (10) 3.4 Apply the designed axiomatic system to a specific tutoring scenario, demonstrating how the axioms guide logical reasoning and decision-making processes. Showcase how the system's feedback aligns with the underlying axioms. Additionally, discuss potential challenges or limitations the system might encounter in real-world tutoring situations, emphasizing areas where the axiomatic system may require refinement or enhancement. (10)

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