PhD Proposal: A Category Theoretic Approach to Planning in a Complex World
Artificial intelligence (AI) planning has become a crucial component in the development of intelligent systems, facilitating the generation and adaptation of plans to achieve specific goals in complex environments. This thesis addresses the challenge of task planning in complex domains, especially ones with a large number of objects and properties, rich relations and dependencies, and incomplete or evolving knowledge. Our approach aims to tackle three specific problems: the difficulty in expressing complex and structured world states, the challenges in reasoning about transitive relations, and the integration of AI components for neurosymbolic reasoning. To address these issues, we propose a novel language called AlgebraicPlanning, based on C-sets and DPO rewriting from category theory. This language uses the expressive power of ontology-based typed graphs to capture complex world states and the relationships within them. We hypothesize that our planning framework will yield higher quality plans and enhance the applicability of task planning in complex real-world domains relative to existing planners. To validate this, we will design a method for assessing the plan length, stability, success rate, and efficiency of plans generated by our framework compared to other planning algorithms. We will also explore the application of our approach in diverse domains, such as classical planning domains, manufacturing, and home service robotics. The contributions of this thesis are expected to include (i) a robust language for representing complex world states, (ii) a planning algorithm based on this formalism, (iii) a method for plan quality assessment, (iv) diverse case studies, and an (v) application of category theory in AI planning. These advancements will pave the way for more robust and adaptive intelligent systems capable of navigating and executing tasks in complex environments.
Dr. William Regli
Dr. John Aloimonos
Dr. Dana Nau
Dr. Mark Fuge