 On the proof-centered approach to logical consequence, the validity of an argument amounts to there being a proof of the conclusions from the premises. Exactly what proofs are is a big issue but the idea is fairly plain (at least if you have been exposed to some proof system or other). Proofs are made up of small steps, the primitive inference principles of the proof system. The 20th Century has seen very many different kinds of proof systems, from so-called Hilbert proofs, with simple rules and complex axioms, to natural deduction systems, with few (or even no) axioms and very many rules.