{"id":"https://openalex.org/W2040792231","doi":"https://doi.org/10.1093/jigpal/jzq006","title":"Permissive nominal terms and their unification: an infinite, co-infinite approach to nominal techniques","display_name":"Permissive nominal terms and their unification: an infinite, co-infinite approach to nominal techniques","publication_year":2010,"publication_date":"2010-05-25","ids":{"openalex":"https://openalex.org/W2040792231","doi":"https://doi.org/10.1093/jigpal/jzq006","mag":"2040792231"},"language":"en","primary_location":{"id":"doi:10.1093/jigpal/jzq006","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzq006","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2312.15651","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073164575","display_name":"Gilles Dowek","orcid":"https://orcid.org/0000-0001-6253-935X"},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]}],"countries":["FR","GB"],"is_corresponding":true,"raw_author_name":"Gilles Dowek","raw_affiliation_strings":["a\u00c9cole Polytechnique, Paris, France and bHeriot-Watt University, Scotland, UK","\u00c9cole Polytechnique, Paris, France and bHeriot-Watt University, Scotland, UK"],"affiliations":[{"raw_affiliation_string":"a\u00c9cole Polytechnique, Paris, France and bHeriot-Watt University, Scotland, UK","institution_ids":["https://openalex.org/I32062511"]},{"raw_affiliation_string":"\u00c9cole Polytechnique, Paris, France and bHeriot-Watt University, Scotland, UK","institution_ids":["https://openalex.org/I32062511","https://openalex.org/I142476485"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022313675","display_name":"Murdoch J. Gabbay","orcid":"https://orcid.org/0000-0001-5796-3455"},"institutions":[{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR","GB"],"is_corresponding":false,"raw_author_name":"Murdoch J. Gabbay","raw_affiliation_strings":["a\u00c9cole Polytechnique, Paris, France and bHeriot-Watt University, Scotland, UK","\u00c9cole Polytechnique, Paris, France and bHeriot-Watt University, Scotland, UK"],"affiliations":[{"raw_affiliation_string":"a\u00c9cole Polytechnique, Paris, France and bHeriot-Watt University, Scotland, UK","institution_ids":["https://openalex.org/I32062511"]},{"raw_affiliation_string":"\u00c9cole Polytechnique, Paris, France and bHeriot-Watt University, Scotland, UK","institution_ids":["https://openalex.org/I32062511","https://openalex.org/I142476485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077355709","display_name":"Dominic P. Mulligan","orcid":"https://orcid.org/0000-0003-4643-3541"},"institutions":[{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR","GB"],"is_corresponding":false,"raw_author_name":"Dominic P. Mulligan","raw_affiliation_strings":["a\u00c9cole Polytechnique, Paris, France and bHeriot-Watt University, Scotland, UK","\u00c9cole Polytechnique, Paris, France and bHeriot-Watt University, Scotland, UK"],"affiliations":[{"raw_affiliation_string":"a\u00c9cole Polytechnique, Paris, France and bHeriot-Watt University, Scotland, UK","institution_ids":["https://openalex.org/I32062511"]},{"raw_affiliation_string":"\u00c9cole Polytechnique, Paris, France and bHeriot-Watt University, Scotland, UK","institution_ids":["https://openalex.org/I32062511","https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073164575"],"corresponding_institution_ids":["https://openalex.org/I142476485","https://openalex.org/I32062511"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":6.9821,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.9673269,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"18","issue":"6","first_page":"769","last_page":"822"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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":0.9998000264167786,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9986000061035156,"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":0.9929999709129333,"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/unification","display_name":"Unification","score":0.8676745295524597},{"id":"https://openalex.org/keywords/permissive","display_name":"Permissive","score":0.5632725954055786},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5446379780769348},{"id":"https://openalex.org/keywords/substitution","display_name":"Substitution (logic)","score":0.5309882760047913},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5085793733596802},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4881752133369446},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4722822606563568},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.42984724044799805},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4197947382926941},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.32568979263305664},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2606222629547119},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.18524029850959778},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06688198447227478},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.055475980043411255}],"concepts":[{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.8676745295524597},{"id":"https://openalex.org/C15224491","wikidata":"https://www.wikidata.org/wiki/Q7169338","display_name":"Permissive","level":2,"score":0.5632725954055786},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5446379780769348},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.5309882760047913},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5085793733596802},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4881752133369446},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4722822606563568},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.42984724044799805},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4197947382926941},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.32568979263305664},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2606222629547119},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.18524029850959778},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06688198447227478},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.055475980043411255},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1093/jigpal/jzq006","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzq006","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2312.15651","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.15651","pdf_url":"https://arxiv.org/pdf/2312.15651","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.185.3105","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.185.3105","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.gabbay.org.uk/papers/perntu-jv.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2312.15651","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.15651","pdf_url":"https://arxiv.org/pdf/2312.15651","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.41999998688697815}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2040792231.pdf","grobid_xml":"https://content.openalex.org/works/W2040792231.grobid-xml"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W123385528","https://openalex.org/W600819829","https://openalex.org/W1483170865","https://openalex.org/W1557497390","https://openalex.org/W1583295953","https://openalex.org/W1594084984","https://openalex.org/W1634581701","https://openalex.org/W1661076342","https://openalex.org/W1819979866","https://openalex.org/W1975082667","https://openalex.org/W1975808446","https://openalex.org/W1979665692","https://openalex.org/W2009464583","https://openalex.org/W2027132261","https://openalex.org/W2028929017","https://openalex.org/W2050702141","https://openalex.org/W2062446527","https://openalex.org/W2064236106","https://openalex.org/W2075352622","https://openalex.org/W2076703601","https://openalex.org/W2088018993","https://openalex.org/W2102472454","https://openalex.org/W2105683431","https://openalex.org/W2108244515","https://openalex.org/W2108640219","https://openalex.org/W2131034879","https://openalex.org/W2134022633","https://openalex.org/W2136171121","https://openalex.org/W2157450565","https://openalex.org/W2161033077","https://openalex.org/W2168547990","https://openalex.org/W2172176924","https://openalex.org/W2180471721","https://openalex.org/W2182660693","https://openalex.org/W2569620744","https://openalex.org/W2599848827","https://openalex.org/W2747549323","https://openalex.org/W2894639777","https://openalex.org/W2911271085","https://openalex.org/W2912255765","https://openalex.org/W3004991051","https://openalex.org/W4212868911","https://openalex.org/W4230919050","https://openalex.org/W4233163177","https://openalex.org/W4237428230","https://openalex.org/W4285719527","https://openalex.org/W4394639621","https://openalex.org/W6604968745","https://openalex.org/W6628563569","https://openalex.org/W6636702598","https://openalex.org/W6636778308","https://openalex.org/W6638742929","https://openalex.org/W6644110450","https://openalex.org/W6644116811","https://openalex.org/W6652624700","https://openalex.org/W6742763569"],"related_works":["https://openalex.org/W2118512822","https://openalex.org/W2152678253","https://openalex.org/W4311090678","https://openalex.org/W3090890720","https://openalex.org/W13526662","https://openalex.org/W4210463230","https://openalex.org/W2996143244","https://openalex.org/W2367630557","https://openalex.org/W3193963519","https://openalex.org/W4231241026"],"abstract_inverted_index":{"Nominal":[0],"terms":[1,4,70,74,144,153],"extend":[2],"first-order":[3],"with":[5],"binding.":[6],"They":[7],"lack":[8],"some":[9],"properties":[10],"of":[11,24,60,104,117,142],"first-":[12],"and":[13,80,86,101,138,147,155,166,179,185],"higher-order":[14,167],"terms:":[15],"Terms":[16],"must":[17],"be":[18],"reasoned":[19],"about":[20],"in":[21,81,181,188],"a":[22,34,39,49,182],"context":[23],"\u2018freshness":[25],"assumptions\u2019;":[26],"it":[27,42],"is":[28,43,62,99,106,130],"not":[29,44,63,131],"always":[30,45],"possible":[31,46],"to":[32,47,54,134,173],"\u2018choose":[33],"fresh":[35],"variable":[36,51],"symbol\u2019":[37,52],"for":[38],"nominal":[40,69,73,114,143,152,164,176],"term;":[41],"\u2018\u03b1-convert":[48],"bound":[50],"or":[53],"\u2018quotient":[55],"by":[56],"\u03b1-equivalence\u2019;":[57],"the":[58,83,91,102,135,160],"notion":[59,103,116],"unifier":[61,105],"based":[64,107,119],"just":[65],"on":[66,108,113,120],"substitution.":[67],"Permissive":[68],"closely":[71],"resemble":[72],"but":[75],"they":[76],"recover":[77],"these":[78],"properties,":[79],"particular":[82],"\u2018always":[84,87],"fresh\u2019":[85],"rename\u2019":[88],"properties.":[89],"In":[90],"permissive":[92,136,151,163,175],"world,":[93],"freshness":[94,124],"contexts":[95],"are":[96],"elided,":[97],"equality":[98],"fixed,":[100],"substitution":[109,121],"alone":[110],"rather":[111],"than":[112],"terms\u2019":[115],"unification":[118,145,165,177],"plus":[122],"extra":[123],"conditions.":[125],"We":[126,158,170],"prove":[127],"that":[128],"expressivity":[129],"lost":[132],"moving":[133],"case":[137],"provide":[139],"an":[140],"injection":[141],"problems":[146,154,178],"their":[148,156],"solutions":[149,180],"into":[150],"solutions.":[157],"investigate":[159],"relation":[161],"between":[162],"pattern":[168],"unification.":[169],"show":[171],"how":[172],"translate":[174],"sound,":[183],"complete,":[184],"optimal":[186],"manner,":[187],"suitable":[189],"senses":[190],"which":[191],"we":[192],"make":[193],"formal.":[194]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-07T14:57:38.498316","created_date":"2016-06-24T00:00:00"}
