{"id":"https://openalex.org/W2040259072","doi":"https://doi.org/10.2307/2274956","title":"Principal type-schemes and condensed detachment","display_name":"Principal type-schemes and condensed detachment","publication_year":1990,"publication_date":"1990-03-01","ids":{"openalex":"https://openalex.org/W2040259072","doi":"https://doi.org/10.2307/2274956","mag":"2040259072"},"language":"en","primary_location":{"id":"doi:10.2307/2274956","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274956","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/A5108383928","display_name":"J. Roger Hindley","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Roger Hindley","raw_affiliation_strings":["Mathematics Division, University College, Swansea SA2 8PP, Wales"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Division, University College, Swansea SA2 8PP, Wales","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034689362","display_name":"David Meredith","orcid":"https://orcid.org/0000-0002-9601-5017"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David Meredith","raw_affiliation_strings":["Old Blood Road, Merrimack, New Hampshire 03054"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Old Blood Road, Merrimack, New Hampshire 03054","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7859,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.93574436,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"55","issue":"1","first_page":"90","last_page":"105"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9980000257492065,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.988099992275238,"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/combinatory-logic","display_name":"Combinatory logic","score":0.9085482358932495},{"id":"https://openalex.org/keywords/modus-ponens","display_name":"Modus ponens","score":0.8936372995376587},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6364254951477051},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5920187830924988},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5708808898925781},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.5694229006767273},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.5278910398483276},{"id":"https://openalex.org/keywords/rule-of-inference","display_name":"Rule of inference","score":0.4995267391204834},{"id":"https://openalex.org/keywords/substitution","display_name":"Substitution (logic)","score":0.4891398251056671},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.4656197726726532},{"id":"https://openalex.org/keywords/syllogism","display_name":"Syllogism","score":0.441205769777298},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.42627936601638794},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40981900691986084},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.40450745820999146},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37924885749816895},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2814673185348511},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2198096513748169},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2164071500301361},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.2075081467628479},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.16729837656021118},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.16264599561691284},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.10716411471366882}],"concepts":[{"id":"https://openalex.org/C79678938","wikidata":"https://www.wikidata.org/wiki/Q1481571","display_name":"Combinatory logic","level":2,"score":0.9085482358932495},{"id":"https://openalex.org/C193885149","wikidata":"https://www.wikidata.org/wiki/Q655742","display_name":"Modus ponens","level":3,"score":0.8936372995376587},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6364254951477051},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5920187830924988},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5708808898925781},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.5694229006767273},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.5278910398483276},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.4995267391204834},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.4891398251056671},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.4656197726726532},{"id":"https://openalex.org/C131598440","wikidata":"https://www.wikidata.org/wiki/Q107342","display_name":"Syllogism","level":2,"score":0.441205769777298},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.42627936601638794},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40981900691986084},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.40450745820999146},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37924885749816895},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2814673185348511},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2198096513748169},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2164071500301361},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.2075081467628479},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.16729837656021118},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.16264599561691284},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.10716411471366882},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2274956","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274956","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:CULeuclid:euclid.jsl/1183743187","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183743187","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W159082583","https://openalex.org/W1523047387","https://openalex.org/W1911287697","https://openalex.org/W1968532969","https://openalex.org/W1972145536","https://openalex.org/W1976353188","https://openalex.org/W1979324125","https://openalex.org/W2010717019","https://openalex.org/W2019376542","https://openalex.org/W2034589435","https://openalex.org/W2049731821","https://openalex.org/W2053760476","https://openalex.org/W2055468395","https://openalex.org/W2064417671","https://openalex.org/W2100539522","https://openalex.org/W2100738443","https://openalex.org/W2141568518","https://openalex.org/W4249075482","https://openalex.org/W6666997118","https://openalex.org/W6830820625"],"related_works":["https://openalex.org/W2022434570","https://openalex.org/W2040259072","https://openalex.org/W1992256554","https://openalex.org/W2579853059","https://openalex.org/W2019107819","https://openalex.org/W2340650165","https://openalex.org/W4385442957","https://openalex.org/W2551561592","https://openalex.org/W2980200192","https://openalex.org/W2143786699"],"abstract_inverted_index":{"The":[0,60],"condensed":[1],"detachment":[2],"rule":[3,6,45,90,104,198],",":[4,8],"or":[5],"D":[7,46,61,91,105,128,142,199],"was":[9],"first":[10],"proposed":[11],"by":[12,80,89,175,197],"Carew":[13],"Meredith":[14],"in":[15,50,118,167,207,217,221,226,234],"the":[16,51,78,94,154,176,204,235,255],"1950's":[17],"for":[18,65,114,131,145,215,257],"propositional":[19,99,218],"logic":[20,100,219],"based":[21],"on":[22],"implication.":[23],"It":[24,189],"is":[25,72,129,143,158,186,213],"a":[26,32,40,66],"combination":[27],"of":[28,35,44,69,179],"modus":[29,81,180],"ponens":[30,82,181],"with":[31],"\u201cminimal\u201d":[33],"amount":[34],"substitution.":[36],"We":[37,137,244],"shall":[38,125,138,202],"give":[39],"precise":[41,205],"detailed":[42],"statement":[43],".":[47],"(Some":[48],"attempts":[49],"published":[52],"literature":[53],"to":[54,108,111,160,165,241,246,249],"do":[55],"this":[56,122,185],"have":[57],"been":[58],"inaccurate.)":[59],"-":[62],"completeness":[63],"question":[64],"given":[67],"set":[68],"logical":[70],"axioms":[71,79],"whether":[73],"every":[74],"formula":[75],"deducible":[76],"from":[77],"and":[83,101,133,150,182,220,254,260],"substitution":[84],"can":[85],"be":[86],"deduced":[87],"instead":[88],"alone.":[92],"Under":[93],"well-known":[95],"formulae-as-types":[96,155],"correspondence":[97,156,206],"between":[98],"combinator-based":[102],"type-theory,":[103],"turns":[106],"out":[107],"correspond":[109,164],"exactly":[110],"an":[112],"algorithm":[113],"computing":[115],"principal":[116],"type-schemes":[117],"combinatory":[119,222],"logic.":[120,136,169,223],"Using":[121],"fact,":[123],"we":[124,194,201,237],"show":[126,140],"that":[127,141,162],"complete":[130],"intuitionistic":[132],"classical":[134],"implicational":[135,168],"also":[139],"incomplete":[144],"two":[146],"weaker":[147],"systems,":[148],"BCK-":[149],"BCI-logic.":[151],"In":[152],"describing":[153],"it":[157],"common":[159],"say":[161,195],"combinators":[163],"proofs":[166],"But":[170],"if":[171],"\u201cproofs\u201d":[172],"means":[173],"\u201cproofs":[174,196],"usual":[177],"rules":[178],"substitution\u201d,":[183],"then":[184],"not":[187,230],"true.":[188],"only":[190],"becomes":[191],"true":[192],"when":[193],"\u201d;":[200],"describe":[203],"Corollary":[208],"6.7.1":[209],"below.":[210],"This":[211],"paper":[212],"written":[214],"readers":[216],"Since":[224],"workers":[225],"one":[227],"field":[228],"may":[229],"feel":[231],"totally":[232],"happy":[233],"other,":[236],"include":[238],"short":[239],"introductions":[240],"both":[242],"fields.":[243],"wish":[245],"record":[247],"thanks":[248],"Martin":[250],"Bunder,":[251],"Adrian":[252],"Rezus":[253],"referee":[256],"helpful":[258],"comments":[259],"advice.":[261]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
