Key research themes
1. How do forward and backward chaining strategies affect learning of geometry theorem proving with construction?
This theme explores the comparative efficacy of forward chaining (FC) and backward chaining (BC) problem-solving strategies in teaching students how to construct geometric proofs involving constructions. It is significant as theorem proving with construction is a challenging skill, and optimizing instructional strategies using intelligent tutoring systems can accelerate student learning.
2. What are the roles and properties of forward adjacency matrices and their inverses in representing directed acyclic graphs (trees)?
This theme investigates a special matrix called the forward adjacency matrix, defined for connected, acyclic directed graphs (trees), where node numbering reflects graph directionality. The matrix entries (0, 1, -1) encode connectivity and direction. Understanding the properties of this matrix and its inverse is vital in graph theory and network analysis, with applications in circuit theory and state space modeling.
3. How can forward chaining methods be effectively applied in expert systems for diagnostic reasoning and knowledge representation?
This theme focuses on the deployment of forward chaining—a data-driven reasoning approach—in expert systems for automated diagnosis and problem solving. Forward chaining starts with known facts and applies inference rules to reach conclusions, contrasted with backward chaining that starts from goals. Its practical utility spans expert systems in medical diagnosis, failure detection, and knowledge-based applications.