The authors' approach to teaching higher-order logic using Isabelle can be extended to cover other advanced topics in logic and formal reasoning by following a similar structured and systematic methodology. For teaching type theory, the approach can involve introducing the foundational concepts of types, type systems, and type inference, building on the basic principles of higher-order logic. This extension would require defining type constructors, type variables, and type rules within the Isabelle framework, similar to how logical connectives and quantifiers were defined in the higher-order logic formalization.
When it comes to modal logics, the approach can focus on introducing modal operators, such as necessity and possibility, and defining the semantics and proof rules associated with modal logic within Isabelle. The formalization would involve incorporating modal axioms and modal inference rules, allowing students to reason about modal properties and modalities using the Isabelle proof assistant.
By structuring the teaching of these advanced topics in a similar manner to the higher-order logic formalization, students can gradually build their understanding from foundational concepts to more complex logical systems. Providing clear explanations, sample proofs, and interactive exercises within Isabelle can enhance the learning experience and help students grasp the intricacies of type theory and modal logics effectively.