Problem Frames as Computational States: A Theory of Endogenous Inquiry

Abstract

Most intelligent systems are evaluated after a problem has been specified: variables, goals, actions, evaluation rules, and hypothesis language are fixed. We study the case in which those commitments can be computational states. A problem frame is a tuple of variables, relations, goals, constraints, actions, validation rules, and a solver class; endogenous inquiry is an evidence-driven transition between frames. We prove a Bayes-risk separation for information-deficient frames, a variational existence result for minimal adequate reframing, a finite-sample identification bound under separating interventions, a multi-frame no-free-reframing limit, and a flattening result characterizing when frame search collapses to model selection. We introduce Endogenous Inquiry Computing (EIC) and EICBench, a benchmark suite pairing five defects with controls and extending them with candidate-set scaling, a two-edit task, symbolic construction of an interaction variable, and a stress test on the Wisconsin breast-cancer dataset. Across 250 defective instances, EIC-Greedy raises performance from 0.360 to 0.964 while making no false reframes in 250 controls. Experiments expose limits: one-edit greedy search fails on a two-edit task, while beam reframing recovers it, and symbolic generation succeeds where raw-feature search does not. Results motivate EIC without claiming problem finding, belief revision, causal discovery, or model selection are new.