Presenting intuitive deductions via symmetric simplification

Abstract

In automated deduction systems that are intended for human use, the presentation of a proof is no less important than its discovery. For most of today’s automated theorem proving systems, this requires a non-trivial translation procedure to extract human-oriented deductions from machine-oriented proofs. Previously known translation procedures, though complete, tend to produce unintuitive deductions. One of the major flaws in such procedures is that too often the rule of indirect proof is used where the introduction of a lemma would result in a shorter and more intuitive proof. We present an algorithm, symmetric simplification, for discovering useful lemmas in deductions of theorems in first- and higher-order logic. This algorithm, which has been implemented in the TPS system, has the feature that resulting deductions may no longer have the weak subformula property. It is currently limited, however, in that it only generates lemmas of the form C V ¬C′, where C and C’ have the same negation normal form.