Getting Saturated with Induction
Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search framework of first-order theorem proving. We describe our inductio...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2024-02 |
|---|---|
| Hauptverfasser: | , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Hajdu, Márton Hozzová, Petra Kovács, Laura Reger, Giles Voronkov, Andrei |
| description | Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search framework of first-order theorem proving. We describe our induction inference rules proving properties with inductively defined datatypes and integers. We also present additional reasoning heuristics for strengthening inductive reasoning, as well as for using induction hypotheses and recursive function definitions for guiding induction. We present exhaustive experimental results demonstrating the practical impact of our approach as implemented within Vampire. This is an extended version of a Principles of Systems Design 2022 paper with the same title and the same authors. |
| doi_str_mv | 10.48550/arxiv.2402.18954 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_2402_18954</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2933661761</sourcerecordid><originalsourceid>FETCH-LOGICAL-a521-b27842f2fe2e96f9d4f24d6a1723a5a7d7408246180bf5d5b29520271d942873</originalsourceid><addsrcrecordid>eNotj81KAzEYRYMgWGofwJUDrmdMvuTLz1KK1kLBRd2HjEk0RWdqJuPP2zttXd3N4XAuIVeMNkIj0luXf9JXA4JCw7RBcUZmwDmrtQC4IIth2FFKQSpA5DNSrUIpqXuttq6M2ZXgq-9U3qp158eXkvrukpxH9z6Exf_Oyfbh_nn5WG-eVuvl3aZ2CKxuQU3-CDFAMDIaLyIILx1TwB065ZWgGoRkmrYRPbZgECgo5o0ArficXJ-sx3q7z-nD5V97eGGPLybi5kTsc_85hqHYXT_mbkqyYDiXkinJ-B94_UeN</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2933661761</pqid></control><display><type>article</type><title>Getting Saturated with Induction</title><source>arXiv.org</source><source>Free E- Journals</source><creator>Hajdu, Márton ; Hozzová, Petra ; Kovács, Laura ; Reger, Giles ; Voronkov, Andrei</creator><creatorcontrib>Hajdu, Márton ; Hozzová, Petra ; Kovács, Laura ; Reger, Giles ; Voronkov, Andrei</creatorcontrib><description>Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search framework of first-order theorem proving. We describe our induction inference rules proving properties with inductively defined datatypes and integers. We also present additional reasoning heuristics for strengthening inductive reasoning, as well as for using induction hypotheses and recursive function definitions for guiding induction. We present exhaustive experimental results demonstrating the practical impact of our approach as implemented within Vampire. This is an extended version of a Principles of Systems Design 2022 paper with the same title and the same authors.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.2402.18954</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Computer Science - Logic in Computer Science ; Reasoning ; Recursive functions ; Systems design ; Theorem proving</subject><ispartof>arXiv.org, 2024-02</ispartof><rights>2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,780,881,27904</link.rule.ids><backlink>$$Uhttps://doi.org/10.48550/arXiv.2402.18954$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.1007/978-3-031-22337-2_15$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>Hajdu, Márton</creatorcontrib><creatorcontrib>Hozzová, Petra</creatorcontrib><creatorcontrib>Kovács, Laura</creatorcontrib><creatorcontrib>Reger, Giles</creatorcontrib><creatorcontrib>Voronkov, Andrei</creatorcontrib><title>Getting Saturated with Induction</title><title>arXiv.org</title><description>Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search framework of first-order theorem proving. We describe our induction inference rules proving properties with inductively defined datatypes and integers. We also present additional reasoning heuristics for strengthening inductive reasoning, as well as for using induction hypotheses and recursive function definitions for guiding induction. We present exhaustive experimental results demonstrating the practical impact of our approach as implemented within Vampire. This is an extended version of a Principles of Systems Design 2022 paper with the same title and the same authors.</description><subject>Computer Science - Logic in Computer Science</subject><subject>Reasoning</subject><subject>Recursive functions</subject><subject>Systems design</subject><subject>Theorem proving</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNotj81KAzEYRYMgWGofwJUDrmdMvuTLz1KK1kLBRd2HjEk0RWdqJuPP2zttXd3N4XAuIVeMNkIj0luXf9JXA4JCw7RBcUZmwDmrtQC4IIth2FFKQSpA5DNSrUIpqXuttq6M2ZXgq-9U3qp158eXkvrukpxH9z6Exf_Oyfbh_nn5WG-eVuvl3aZ2CKxuQU3-CDFAMDIaLyIILx1TwB065ZWgGoRkmrYRPbZgECgo5o0ArficXJ-sx3q7z-nD5V97eGGPLybi5kTsc_85hqHYXT_mbkqyYDiXkinJ-B94_UeN</recordid><startdate>20240229</startdate><enddate>20240229</enddate><creator>Hajdu, Márton</creator><creator>Hozzová, Petra</creator><creator>Kovács, Laura</creator><creator>Reger, Giles</creator><creator>Voronkov, Andrei</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>AKY</scope><scope>GOX</scope></search><sort><creationdate>20240229</creationdate><title>Getting Saturated with Induction</title><author>Hajdu, Márton ; Hozzová, Petra ; Kovács, Laura ; Reger, Giles ; Voronkov, Andrei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a521-b27842f2fe2e96f9d4f24d6a1723a5a7d7408246180bf5d5b29520271d942873</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Computer Science - Logic in Computer Science</topic><topic>Reasoning</topic><topic>Recursive functions</topic><topic>Systems design</topic><topic>Theorem proving</topic><toplevel>online_resources</toplevel><creatorcontrib>Hajdu, Márton</creatorcontrib><creatorcontrib>Hozzová, Petra</creatorcontrib><creatorcontrib>Kovács, Laura</creatorcontrib><creatorcontrib>Reger, Giles</creatorcontrib><creatorcontrib>Voronkov, Andrei</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv Computer Science</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hajdu, Márton</au><au>Hozzová, Petra</au><au>Kovács, Laura</au><au>Reger, Giles</au><au>Voronkov, Andrei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Getting Saturated with Induction</atitle><jtitle>arXiv.org</jtitle><date>2024-02-29</date><risdate>2024</risdate><eissn>2331-8422</eissn><abstract>Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search framework of first-order theorem proving. We describe our induction inference rules proving properties with inductively defined datatypes and integers. We also present additional reasoning heuristics for strengthening inductive reasoning, as well as for using induction hypotheses and recursive function definitions for guiding induction. We present exhaustive experimental results demonstrating the practical impact of our approach as implemented within Vampire. This is an extended version of a Principles of Systems Design 2022 paper with the same title and the same authors.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.2402.18954</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2024-02 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_arxiv_primary_2402_18954 |
| source | arXiv.org; Free E- Journals |
| subjects | Computer Science - Logic in Computer Science Reasoning Recursive functions Systems design Theorem proving |
| title | Getting Saturated with Induction |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-26T21%3A02%3A15IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Getting%20Saturated%20with%20Induction&rft.jtitle=arXiv.org&rft.au=Hajdu,%20M%C3%A1rton&rft.date=2024-02-29&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.2402.18954&rft_dat=%3Cproquest_arxiv%3E2933661761%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2933661761&rft_id=info:pmid/&rfr_iscdi=true |