Induction Models on $\mathbb{N}$

22 pages•Published: May 27, 2020

A. Dileep, Kuldeep S. Meel and Ammar F. Sabili

Abstract

Mathematical induction is a fundamental tool in computer science and mathematics. Henkin [12] initiated the study of formalization of mathematical induction restricted to the setting when the base case B is set to singleton set containing 0 and a unary generating function S. The usage of mathematical induction often involves wider set of base cases and k−ary generating functions with different structural restrictions. While subsequent studies have shown several Induction Models to be equivalent, there does not exist precise logical characterization of reduction and equivalence among different Induction Models. In this paper, we generalize the definition of Induction Model and demonstrate existence and construction of S for given B and vice versa. We then provide a formal characterization of the reduction among different Induction Models that can allow proofs in one Induction Models to be expressed as proofs in another Induction Models. The notion of reduction allows us to capture equivalence among Induction Models.

Keyphrases: equivalence, induction models, mathematical induction, reduction

In: Elvira Albert and Laura Kovacs (editors). LPAR23. LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 73, pages 169-190.

Links:	https://easychair.org/publications/paper/3WMv
	https://doi.org/10.29007/kvp3

BibTeX entry

@inproceedings{LPAR23:Induction_Models_$\mathbb{N}$,
  author    = {A. Dileep and Kuldeep S. Meel and Ammar F. Sabili},
  title     = {Induction Models on $\mathbb{N}$},
  booktitle = {LPAR23. LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Elvira Albert and Laura Kovacs},
  series    = {EPiC Series in Computing},
  volume    = {73},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/3WMv},
  doi       = {10.29007/kvp3},
  pages     = {169-190},
  year      = {2020}}

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