Reasoning, Metareasoning, and Mathematical Truth: Studies of Theorem Proving under Limited Resources

In earlier work, we introduced flexible infer­ ence and decision-theoretic metareasoning to address the intractability of normative infer­ ence. Here, rather than pursuing the task of computing beliefs and actions with decision models composed of distinctions about uncer­ tain events, we examine methods for inferring beliefs about mathematical truth before an automated theorem prover completes a proof. We employ a Bayesian analysis to update be­ lief in truth, given theorem-proving progress, and show how decision-theoretic methods can be used to determine the value of continuing to deliberate versus taking immediate action in time-critical situations.