On the Inherent Necessity of Heuristic Proofs
Stuart H. Rubin, Shu‐Ching Chen, James Law, G.K. Lee · 2006
It follows from the nonreducibility of the theorization problem that an arbitrary proof cannot be valid on an absolute scale. Thus, in order for an arbitrary proof to be generative, it must be self-referential; but then, it must also be heuristic if not incomplete as a consequence. By relaxing the validity requirement, heuristic (i.e., relative) proof techniques are enabled. We show that heuristics are search randomizations in space-time. It is shown how one can develop heuristics, which are randomizations of knowledge. Even more intriguing, it is shown that heuristic proof is to formal proof what fuzzy logic is to formal logic. Simply put, the paper argues for the need to relax the notion of formal proof if AI is to advance.