A Unified View of Induction Reasoning for First-Order Logic

27 pages•Published: June 22, 2012

Abstract

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.

Keyphrases: explicit induction, implicit induction, induction theorem proving

In: Andrei Voronkov (editor). Turing-100. The Alan Turing Centenary, vol 10, pages 326-352.

Links:	https://easychair.org/publications/paper/4qw
	https://doi.org/10.29007/nsx4