Axioms or algorithms

Abstract

Traditional formal proof systems have been found unusable by those working on such applications of logic as program verification. They demand too much from the proof generator and too little from the proof checker. The notion of proof sketch or informal proof is an unsatisfactory substitute both because it is imprecise and because it treats the symptom rather than the disease. We propose to replace axiomatic proof systems by algorithmic proof systems, which explicitly incorporate a quantitative notion of computational complexity. This proposal depends on the existence of tractable decision procedures for many substantial fragments of logic, the "easy fragments."