Chain-of-Feasibility: A Knowledge Refinement Framework for Ill-Defined Problems

Many reasoning problems are ill-defined. Goals, constraints, and acceptable solutions are not fully specified at the outset and emerge only through attempted constructions and failures. We introduce Chain-of-Feasibility, a knowledge refinement framework that models reasoning progress as iterative restriction of a feasible solution space. The framework represents partial approaches, constraints, and failures as explicit epistemic artifacts stored in a persistent structure. Feasibility is defined constructively, combining constraint satisfaction with representational availability. We provide a formal account, prove monotonicity and termination properties, embed Reiter's diagnosis as a special case, and demonstrate operational instantiations showing epistemic invariance across execution strategies.