'Descente Infinie' Induction-Based Saturation Procedures

Abstract

In [11], we have shown that implicit induction and saturation proof techniques share the same logic, witnessed by an inference system implementing the Fermat's 'Descente Infinie' induction principle. As a case study, a simple paramodulation-based inference system has been proved as an instance of it. In this paper, we detail the instantiation method to treat general saturation-based systems and apply it to analyse a non-trivial resolution-based system. We also propose a methodology to build variants of existing systems, which preserve crucial properties like soundness and refutational completeness.

Automated Certification of Implicit Induction Proofs

“…In this case, the Noetherian induction principle becomes a contrapositive version of the 'Descente Infinie' induction principle we have previously used in [20,21,22,23]:…”

A Unified View of Induction Reasoning for First-Order Logic

“…If the set of new conjectures is not empty, the current conjecture is saved as premise. φ[r i ] p indicates that φ has the subterm r i at position p. In [48,49], it has been shown that ∪ n i {φ i } from similar superposition-based inference rules is a strict cover set of φ, as it is the case for ConjSup.…”

“…It is conducted by a methodology to build sound implicit induction procedures using the compositional properties of contextual cover sets. The methodology also allowed to represent saturation-based inference systems as instances of the general inference system [48,49]. It witnesses that the implicit induction and saturation-based procedures share the same logic.…”