Some observations on the logical foundations of inductive theorem proving

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a goal. Based on this model, we then analyze the following aspec...

Full description

Saved in:
Bibliographic Details
Published in:Logical methods in computer science Vol. 13, Issue 4; no. Automated deduction
Main Authors: Hetzl, Stefan, Wong, Tin Lok
Format: Journal Article
Language:English
Published: Logical Methods in Computer Science e.V 01.01.2017
Subjects:
computer science - logic in computer science
mathematics - logic
ISSN:1860-5974, 1860-5974
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a goal. Based on this model, we then analyze the following aspects: the choice of a proof shape, the choice of an induction rule and the language of the induction formula. In particular, using model-theoretic techniques, we clarify the relationship between notions of inductiveness that have been considered in the literature on automated inductive theorem proving. This is a corrected version of the paper arXiv:1704.01930v5 published originally on Nov.~16, 2017.
AbstractList In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a goal. Based on this model, we then analyze the following aspects: the choice of a proof shape, the choice of an induction rule and the language of the induction formula. In particular, using model-theoretic techniques, we clarify the relationship between notions of inductiveness that have been considered in the literature on automated inductive theorem proving. This is a corrected version of the paper arXiv:1704.01930v5 published originally on Nov.~16, 2017.
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a goal. Based on this model, we then analyze the following aspects: the choice of a proof shape, the choice of an induction rule and the language of the induction formula. In particular, using model-theoretic techniques, we clarify the relationship between notions of inductiveness that have been considered in the literature on automated inductive theorem proving.
Author Wong, Tin Lok
Hetzl, Stefan
Author_xml – sequence: 1
  givenname: Stefan
  orcidid: 0000-0002-6461-5982
  surname: Hetzl
  fullname: Hetzl, Stefan
– sequence: 2
  givenname: Tin Lok
  surname: Wong
  fullname: Wong, Tin Lok
BookMark eNpNkMtOwzAQRS0EEqX0B1hlCYvA-BHHYYcqHpWKWBTWlmOPi6s0rpy0En9P2gJiNjO6M3N0dS_IaRtbJOSKwi3jkqu7-et0kVN-Le4p3DCg5QkZUSUhL6pSnP6bz8mk61YwFOdUMTkis0VcYxbrDtPO9CG2XRbbrP_ErInLYE2T-bht3e_KZ6F1W9uHHe6PYsJ1tklxF9rlJTnzpulw8tPH5OPp8X36ks_fnmfTh3luOag-F9YhL_xgsvKVQJDSlbWB0qEylbGioMikYkyWICRYVACWmtpRR2vLLPAxmR25LpqV3qSwNulLRxP0QYhpqU3qg21QF4rXw4vgtecCpFKFNwKYNdwWwkkcWOzIsil2XUL_x6OgD9nqfbaaci0O0mCbfwO2Q27T
ContentType Journal Article
DBID AAYXX
CITATION
DOA
DOI 10.23638/LMCS-13(4:10)2017
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EISSN 1860-5974
ExternalDocumentID oai_doaj_org_article_583b2c043bf3406885fa402ca3c54d6e
10_23638_LMCS_13_4_10_2017
GroupedDBID .4S
.DC
29L
2WC
5GY
5VS
AAFWJ
AAYXX
ADBBV
ADMLS
ADQAK
AENEX
AFPKN
ALMA_UNASSIGNED_HOLDINGS
ARCSS
BCNDV
CITATION
EBS
EJD
FRP
GROUPED_DOAJ
J9A
KQ8
MK~
ML~
M~E
OK1
OVT
P2P
TR2
TUS
XSB
ID FETCH-LOGICAL-c308t-4cde35f0179f94e066d7ba07de8a9ac451e26822670460ce800c1abd1d1bc2c03
IEDL.DBID DOA
ISICitedReferencesCount 4
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000419167900016&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1860-5974
IngestDate Fri Oct 03 12:54:03 EDT 2025
Sat Nov 29 08:05:09 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue Automated deduction
Language English
License https://creativecommons.org/licenses/by/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c308t-4cde35f0179f94e066d7ba07de8a9ac451e26822670460ce800c1abd1d1bc2c03
ORCID 0000-0002-6461-5982
OpenAccessLink https://doaj.org/article/583b2c043bf3406885fa402ca3c54d6e
ParticipantIDs doaj_primary_oai_doaj_org_article_583b2c043bf3406885fa402ca3c54d6e
crossref_primary_10_23638_LMCS_13_4_10_2017
PublicationCentury 2000
PublicationDate 2017-01-01
PublicationDateYYYYMMDD 2017-01-01
PublicationDate_xml – month: 01
  year: 2017
  text: 2017-01-01
  day: 01
PublicationDecade 2010
PublicationTitle Logical methods in computer science
PublicationYear 2017
Publisher Logical Methods in Computer Science e.V
Publisher_xml – name: Logical Methods in Computer Science e.V
SSID ssj0000331826
Score 2.0981412
Snippet In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around...
SourceID doaj
crossref
SourceType Open Website
Index Database
SubjectTerms computer science - logic in computer science
mathematics - logic
Title Some observations on the logical foundations of inductive theorem proving
URI https://doaj.org/article/583b2c043bf3406885fa402ca3c54d6e
Volume 13, Issue 4
WOSCitedRecordID wos000419167900016&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAON
  databaseName: DOAJ Directory of Open Access Journals
  customDbUrl:
  eissn: 1860-5974
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000331826
  issn: 1860-5974
  databaseCode: DOA
  dateStart: 20040101
  isFulltext: true
  titleUrlDefault: https://www.doaj.org/
  providerName: Directory of Open Access Journals
– providerCode: PRVHPJ
  databaseName: ROAD: Directory of Open Access Scholarly Resources
  customDbUrl:
  eissn: 1860-5974
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000331826
  issn: 1860-5974
  databaseCode: M~E
  dateStart: 20040101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwELZQxcDCG1Fe8sAAQlaT2I4TNqhagdRWSAWpW-SnxNCk6oOR387ZSasysbBksKPo9J19993FvkPoVlquI24lEdQJwpxNSe6UJCk4G0UTAbOhuv5AjEbZZJK_bbX68mfC6vLANXAdnlGV6IhR5SjzHVK4kxDzaEk1Zya13voC69kKpoINptQT5_qWTEJhkXUGw-6YxPSOPcbRPUgifnmirYL9wbP0D9F-QwnxUy3KEdqx5TE6WLdbwM3uO0Gv42pqcaU2edQFrkoMBA439gu7TY8kmHIYwu1VMGe4vq44xU0C4RR99Hvv3RfSdEIgmkbZkjBtLOXO7x6XMws0wQglI2FsJnOpGY9tkoKrT4X_z6ktsEAdS2ViEysN6NEz1Cqr0p4jrLjyx0ZTm0Hk5aRRLs9YxpPUyEQbp9roYY1KMasLXhQQKAQMC49hEdOChSEQp42ePXCbN32x6jAAKiwaFRZ_qfDiPz5yifa8QHV25Aq1lvOVvUa7-mv5uZjfhNUBz-F37we3_b-4
linkProvider Directory of Open Access Journals
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Some+observations+on+the+logical+foundations+of+inductive+theorem+proving&rft.jtitle=Logical+methods+in+computer+science&rft.au=Hetzl%2C+Stefan&rft.au=Wong%2C+Tin+Lok&rft.date=2017-01-01&rft.issn=1860-5974&rft.eissn=1860-5974&rft.volume=13%2C+Issue+4&rft.issue=Automated+deduction&rft_id=info:doi/10.23638%2FLMCS-13%284%3A10%292017&rft.externalDBID=n%2Fa&rft.externalDocID=10_23638_LMCS_13_4_10_2017
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1860-5974&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1860-5974&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1860-5974&client=summon