Learning Theory and Knowledge Hierarchy for Artificial Intelligence Systems

This work represents a continuation of our research in the realm of building Trustworthy AI and Explainable AI. The paper delves into the learning theory of intelligent systems, drawing upon classical mathematical approaches such as the task-based approach, the concept of semantic programming, computability theory, and model theory. This approach allows us to construct a knowledge base for AI systems, which can then be used to establish a natural hierarchy of knowledge within these systems. This enables AI systems to engage in continuous self-learning, as well as efficiently tackle the specific tasks they are designed for. Furthermore, AI systems can provide logical explanations for their decisions, accompanied by a set of guiding rules. This attribute of explainability, however, is notably absent in many large language models, leading us to explore the concept of hybrid AI systems, where neuro-symbolic AI integrates symbolic AI with neuro-statistical AI.