{"id":"https://openalex.org/W2006177255","doi":"https://doi.org/10.2307/2275674","title":"The undecidability of second order linear logic without exponentials","display_name":"The undecidability of second order linear logic without exponentials","publication_year":1996,"publication_date":"1996-06-01","ids":{"openalex":"https://openalex.org/W2006177255","doi":"https://doi.org/10.2307/2275674","mag":"2006177255"},"language":"en","primary_location":{"id":"doi:10.2307/2275674","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275674","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039362217","display_name":"Yves Lafont","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210138206","display_name":"Institut de Math\u00e9matiques de Marseille","ror":"https://ror.org/042h2y225","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210138206","https://openalex.org/I4210141950","https://openalex.org/I4210142724"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Yves Lafont","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques Discr\u00e8tes, UPR 9016 du CNRS, 163 Avenue de Luminy, Case 930, 13288 Marseille Cedex 9, France, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Discr\u00e8tes, UPR 9016 du CNRS, 163 Avenue de Luminy, Case 930, 13288 Marseille Cedex 9, France, E-mail:","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210138206","https://openalex.org/I4210155549"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039362217"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210138206","https://openalex.org/I4210155549"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":3.8782,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.93785866,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"61","issue":"2","first_page":"541","last_page":"548"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.8703458905220032},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.7430562376976013},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.7160268425941467},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.7009502053260803},{"id":"https://openalex.org/keywords/fragment","display_name":"Fragment (logic)","score":0.691281259059906},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5845852494239807},{"id":"https://openalex.org/keywords/substructural-logic","display_name":"Substructural logic","score":0.48584744334220886},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4815678596496582},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.4585535228252411},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.4463016986846924},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.43786177039146423},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4196133613586426},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.3358275890350342},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28325894474983215},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25345152616500854},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.18029913306236267},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.1309296190738678},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08508890867233276}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.8703458905220032},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.7430562376976013},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7160268425941467},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.7009502053260803},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.691281259059906},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5845852494239807},{"id":"https://openalex.org/C144760519","wikidata":"https://www.wikidata.org/wiki/Q839490","display_name":"Substructural logic","level":4,"score":0.48584744334220886},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4815678596496582},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.4585535228252411},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.4463016986846924},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.43786177039146423},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4196133613586426},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.3358275890350342},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28325894474983215},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25345152616500854},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.18029913306236267},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.1309296190738678},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08508890867233276},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2307/2275674","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275674","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.56.8051","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.8051","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://lmd.univ-mrs.fr/pub/lafont/mall2.ps.Z","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183745013","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745013","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.47999998927116394,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W98010569","https://openalex.org/W1499479569","https://openalex.org/W1575454925","https://openalex.org/W1590029082","https://openalex.org/W1884776640","https://openalex.org/W1966857180","https://openalex.org/W2021289373","https://openalex.org/W2054548224","https://openalex.org/W2061970672","https://openalex.org/W2083147990","https://openalex.org/W2895234266","https://openalex.org/W2911865844","https://openalex.org/W2985950726","https://openalex.org/W4232385252"],"related_works":["https://openalex.org/W2170042182","https://openalex.org/W2183401507","https://openalex.org/W2754467536","https://openalex.org/W2166879872","https://openalex.org/W1784226744","https://openalex.org/W1968027005","https://openalex.org/W2952004916","https://openalex.org/W2021289373","https://openalex.org/W2111490376","https://openalex.org/W2164691248"],"abstract_inverted_index":{"Abstract":[0],"Recently,":[1],"Lincoln,":[2],"Scedrov":[3],"and":[4],"Shankar":[5],"showed":[6],"that":[7,53],"the":[8,31,40,54,86],"multiplicative":[9],"fragment":[10,56],"of":[11,22,57,69,78,85],"second":[12,23,44,58],"order":[13,24,45,59],"intuitionistic":[14,25],"linear":[15,61],"logic":[16,47,62],"is":[17,48,63,81],"undecidable,":[18,65],"using":[19,66],"an":[20,67],"encoding":[21,68,80],"logic.":[26],"Their":[27],"argument":[28],"applies":[29],"to":[30,74],"multiplicative-additive":[32,55],"fragment,":[33],"but":[34],"it":[35],"does":[36],"not":[37],"work":[38],"in":[39],"classical":[41,46,60],"case,":[42],"because":[43],"decidable.":[49],"Here":[50],"we":[51],"show":[52],"also":[64],"two-counter":[70],"machines":[71],"originally":[72],"due":[73],"Kanovich.":[75],"The":[76],"faithfulness":[77],"this":[79],"proved":[82],"by":[83],"means":[84],"phase":[87],"semantics.":[88]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}