A Note on the Complexity of Classical and Intuitionistic Proofs
We show an effective cut-free variant of Glivenko's theorem extended to formulas with weak quantifiers (those without eigenvariable conditions): "There is an elementary function f such that if φ is a cut-free LK proof of ⊢ A with symbol complexity ≤ c, then there exists a cut-free LJ proof...
Uloženo v:
| Vydáno v: | 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science s. 657 - 666 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Konferenční příspěvek |
| Jazyk: | angličtina |
| Vydáno: |
IEEE
01.07.2015
|
| Témata: | |
| ISSN: | 1043-6871 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | We show an effective cut-free variant of Glivenko's theorem extended to formulas with weak quantifiers (those without eigenvariable conditions): "There is an elementary function f such that if φ is a cut-free LK proof of ⊢ A with symbol complexity ≤ c, then there exists a cut-free LJ proof of 1⊢ ⊣⊣A with symbol complexity ≤ f(c)". This follows from the more general result: "There is an elementary function f such that if φ is a cut-free LK proof of A ⊢ with symbol complexity ≤ c, then there exists a cut-free LJ proof of A ⊢ with symbol complexity ≤ f(c)". The result is proved using a suitable variant of cut-elimination by resolution (CERES) and subsumption. |
|---|---|
| AbstractList | We show an effective cut-free variant of Glivenko's theorem extended to formulas with weak quantifiers (those without eigenvariable conditions): "There is an elementary function f such that if φ is a cut-free LK proof of ⊢ A with symbol complexity ≤ c, then there exists a cut-free LJ proof of 1⊢ ⊣⊣A with symbol complexity ≤ f(c)". This follows from the more general result: "There is an elementary function f such that if φ is a cut-free LK proof of A ⊢ with symbol complexity ≤ c, then there exists a cut-free LJ proof of A ⊢ with symbol complexity ≤ f(c)". The result is proved using a suitable variant of cut-elimination by resolution (CERES) and subsumption. |
| Author | Baaz, Matthias Reis, Giselle Leitsch, Alexander |
| Author_xml | – sequence: 1 givenname: Matthias surname: Baaz fullname: Baaz, Matthias email: baaz@logic.at – sequence: 2 givenname: Alexander surname: Leitsch fullname: Leitsch, Alexander email: leitsch@logic.at – sequence: 3 givenname: Giselle surname: Reis fullname: Reis, Giselle email: giselle.reis@inria.fr |
| BookMark | eNotzMtKAzEUANAIFWxrd-7c5Aem3pt3VlIGHwODCuq6xEyCkemkTCLYv3ehq7M7K7KY8hQIuULYIoK96bv2dcsA5VapM7Kx2qDQ1hqjpViQJYLgjTIaL8iqlC8AYErAktzu6FOugeaJ1s9A23w4juEn1RPNkbajKyV5N1I3DbSb6neqKU-p1OTpy5xzLJfkPLqxhM2_a_J-f_fWPjb980PX7vrGcaFqM7BBSgUgP7yJinupGYsgg8cQjJfogA2WO4gDGlAGfUTutDBMi8AG5vmaXP-9KYSwP87p4ObTXqMWlgH_Bd4qSR4 |
| CODEN | IEEPAD |
| ContentType | Conference Proceeding |
| DBID | 6IE 6IH CBEJK RIE RIO |
| DOI | 10.1109/LICS.2015.66 |
| DatabaseName | IEEE Electronic Library (IEL) Conference Proceedings IEEE Proceedings Order Plan (POP) 1998-present by volume IEEE Xplore All Conference Proceedings IEEE Electronic Library (IEL) IEEE Proceedings Order Plans (POP) 1998-present |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISBN | 9781479988754 1479988758 |
| EndPage | 666 |
| ExternalDocumentID | 7174920 |
| Genre | orig-research |
| GroupedDBID | --Z 23M 29P 6IE 6IF 6IH 6IK 6IL 6IM 6IN AAJGR AAWTH ADZIZ ALMA_UNASSIGNED_HOLDINGS BEFXN BFFAM BGNUA BKEBE BPEOZ CBEJK CHZPO IEGSK IJVOP IPLJI M43 OCL RIE RIL RIO RNS |
| ID | FETCH-LOGICAL-a346t-d2d556005bc8f63c5722f05ec1ee8c51a02d93a0fd180681cf13a748274e2d2c3 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 1 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000380427100058&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1043-6871 |
| IngestDate | Wed Aug 27 02:33:32 EDT 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | true |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a346t-d2d556005bc8f63c5722f05ec1ee8c51a02d93a0fd180681cf13a748274e2d2c3 |
| OpenAccessLink | https://inria.hal.science/hal-01208346 |
| PageCount | 10 |
| ParticipantIDs | ieee_primary_7174920 |
| PublicationCentury | 2000 |
| PublicationDate | 20150701 |
| PublicationDateYYYYMMDD | 2015-07-01 |
| PublicationDate_xml | – month: 07 year: 2015 text: 20150701 day: 01 |
| PublicationDecade | 2010 |
| PublicationTitle | 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science |
| PublicationTitleAbbrev | LICS |
| PublicationYear | 2015 |
| Publisher | IEEE |
| Publisher_xml | – name: IEEE |
| SSID | ssj0002640 ssj0002179874 |
| Score | 1.9225767 |
| Snippet | We show an effective cut-free variant of Glivenko's theorem extended to formulas with weak quantifiers (those without eigenvariable conditions): "There is an... |
| SourceID | ieee |
| SourceType | Publisher |
| StartPage | 657 |
| SubjectTerms | Calculus classical logic complexity Complexity theory Computer science Context Geometry Glivenko's theorem intuitionistic logic Merging |
| Title | A Note on the Complexity of Classical and Intuitionistic Proofs |
| URI | https://ieeexplore.ieee.org/document/7174920 |
| WOSCitedRecordID | wos000380427100058&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 | |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV09a8MwEBVp6NCpH0npNxo61oktWZY0lRIaGggh0A-yBUU6QRe7pE6h_746xXU7dOlmjG3MHfJ7J797R8h1yqWREkIGnHdJLn2RGGVXiVgJ4ZhZ5Sb2cb9M5WymFgs975CbthcGAKL4DAZ4GP_lu8pucKtsGEqPXLNQoO9IWWx7tdr9FIbOW0hlmq9wAPrGiYAnRagKWtG7Hk4no0cUdYkBeiP-GqoSMWW8_7-3OSD9n-Y8Om9h55B0oDwi-9_TGWizWHvk9o7OqhpoVdJA8ihegOaX9SetPI2zMDE_1JSOTgLwROlWdG3Gpwdo7JPn8f3T6CFpxiUkhudFnTjmBPIXsbLKF9wKyZhPBdgMQFmRmZQ5zU3qXabSQmXWZ9xItAHNgTlm-THpllUJJ4R64FmmA5VVGnKBfjG60IHquXBLnipzSnoYj-Xb1hFj2YTi7O_T52QPo70VuV6Qbr3ewCXZtR_16_v6KqbxC6Eqmj8 |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1NS8NAEF1KFfRUtRW_3YNH0272I9k9iYilxRgKVumtbPYDvCRSU8F_7-42Rg9evIWQhDDD5r3ZvHkDwBUiqUxT4zKgrY5oapNIclVErGBMY1lQGfq4X7I0z_liIWYdcN32whhjgvjMDP1h-JevK7X2W2UjV3pQgV2BvsUoxWjTrdXuqGDvveXJTPMddlDfeBGQKHF1QSt7F6NsevfkZV1s6N0Rf41VCagy7v3vffbA4Kc9D85a4NkHHVMegN73fAbYLNc-uLmFeVUbWJXQ0TzoL_D2l_UnrCwM0zB9hqAsNZw66AnireDb7J_uwHEAnsf387tJ1AxMiCShSR1prJlnMKxQ3CZEsRRji5hRsTFcsVgirAWRyOqYo4THysZEpt4IlBqssSKHoFtWpTkC0BoSx8KRWS4MZd4xRiTCkT3tbqGIy2PQ9_FYvm08MZZNKE7-Pn0Jdibzx2yZTfOHU7DrI7-RvJ6Bbr1am3OwrT7q1_fVRUjpF9zDnYY |
| 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%3Abook&rft.genre=proceeding&rft.title=2015+30th+Annual+ACM%2FIEEE+Symposium+on+Logic+in+Computer+Science&rft.atitle=A+Note+on+the+Complexity+of+Classical+and+Intuitionistic+Proofs&rft.au=Baaz%2C+Matthias&rft.au=Leitsch%2C+Alexander&rft.au=Reis%2C+Giselle&rft.date=2015-07-01&rft.pub=IEEE&rft.issn=1043-6871&rft.spage=657&rft.epage=666&rft_id=info:doi/10.1109%2FLICS.2015.66&rft.externalDocID=7174920 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1043-6871&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1043-6871&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1043-6871&client=summon |