Proofs, proofs, proofs, and proofs

Abstract

In logic there is a clear concept of what constitutes a proof and what not. A proof is essentially defined as a finite sequence of formulae which are either axioms or derived by proof rules from formulae earlier in the sequence. Sociologically, however, it is more difficult to say what should constitute a proof and what not. In this paper we will look at different forms of proofs and try to clarify the concept of proof in the wider meaning of the term. This has implications on how proofs should be represented formally. © 2010 Springer-Verlag Berlin Heidelberg.