Proving, Refuting, Improving—Looking for a Theorem

Exploring the proofs and refutations of an abstract statement, conjecture with aim to give a formal syntactic treatment its proving–refuting process, we introduce notion extrapolation possibly unprovable statement having form if A, then B, propose procedure that should result in new A′, B′, which is similar starting one, but provable. We think this procedure, based on method, can be considered basic methodological tool applicable prove–refute–improve any conjecture. This notion, extrapolation, presents dual counterpart well-known interpolation introduced traditional logic sixty-five years ago.