Abstract: Exploring the proofs and refutations of an abstract statement, conjecture with the aim to give a formal syntactic treatment of its proving–refuting process, we introduce the notion of extrapolation of a possibly unprovable statement having the form if A, then B, and propose a procedure that should result in the new statement if A 0 , then B 0 , which is similar to the starting one, but provable. We think that this procedure, based on the extrapolation method, can be considered a basic methodological tool applicable to prove–refute–improve any conjecture. This new notion, extrapolation, presents a dual counterpart of the well-known interpolation introduced in traditional logic sixty-five years ago eng application/pdf 255914 bytes http://creativecommons.org/licenses/by/4.0/legalcode 2022 Keywords: extrapolation; interpolation; proving; refuting; improving https://phaidrabg.bg.ac.rs/o:29632 doi:10.3390/axioms11100559 ISSN: 2075-1680 Boričić, Branislav Axioms 11(10) Proving, Refuting, Improving—Looking for a Theorem info:eu-repo/semantics/article