A Unified View of Induction Reasoning for First-Order Logic
Sorin Ioan Stratulat · EPiC series in computing · 2018
Induction is a powerful proof technique adapted to reason on sets with an unbounded number of elements. In a first-order setting, two different methods are distinguished: the conventional induction, based on explicit induction schemas, and the implicit induction, based on reductive procedures. We propose a new cycle-based induction method that keeps their best features, i.e. i) performs lazy induction, ii) naturally fits for mutual induction, and iii) is free of reductive constraints. The heart of the method is a proof strategy that identifies in the proof script the subset of formulas contributing to validate the application of induction hypotheses. The conventional and implicit induction are particular cases of our method.