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A Unified View of Induction Reasoning for First-Order Logic

Sorin Stratulat 1, 2, * 
* Corresponding author
1 PAREO - Formal islands: foundations and applications
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
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., performs local and non-reductive reasoning, and naturally fits for mutual and lazy induction. 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.
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Submitted on : Monday, December 10, 2012 - 1:41:06 PM
Last modification on : Wednesday, February 2, 2022 - 5:00:56 PM
Long-term archiving on: : Saturday, December 17, 2016 - 11:21:10 PM


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  • HAL Id : hal-00763236, version 1



Sorin Stratulat. A Unified View of Induction Reasoning for First-Order Logic. Turing-100, The Alan Turing Centenary Conference, Jun 2012, Manchester, United Kingdom. ⟨hal-00763236⟩



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