{"id":"https://openalex.org/W2157560459","doi":"https://doi.org/10.2307/2274487","title":"A partial functions version of Church's simple theory of types","display_name":"A partial functions version of Church's simple theory of types","publication_year":1990,"publication_date":"1990-09-01","ids":{"openalex":"https://openalex.org/W2157560459","doi":"https://doi.org/10.2307/2274487","mag":"2157560459"},"language":"en","primary_location":{"id":"doi:10.2307/2274487","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274487","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/A5026752114","display_name":"William M. Farmer","orcid":null},"institutions":[{"id":"https://openalex.org/I44896327","display_name":"Mitre (United States)","ror":"https://ror.org/03ks2a131","country_code":"US","type":"company","lineage":["https://openalex.org/I44896327"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"William M. Farmer","raw_affiliation_strings":["The Mitre Corporation, Bedford, Massachusetts 01730"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Mitre Corporation, Bedford, Massachusetts 01730","institution_ids":["https://openalex.org/I44896327"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026752114"],"corresponding_institution_ids":["https://openalex.org/I44896327"],"apc_list":null,"apc_paid":null,"fwci":5.3712,"has_fulltext":false,"cited_by_count":99,"citation_normalized_percentile":{"value":0.95653259,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"55","issue":"3","first_page":"1269","last_page":"1291"},"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9962999820709229,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9733999967575073,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.7520013451576233},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.7199644446372986},{"id":"https://openalex.org/keywords/partial-function","display_name":"Partial function","score":0.7160665988922119},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5100034475326538},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5089190006256104},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.473993182182312},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4599570035934448},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.440615713596344},{"id":"https://openalex.org/keywords/truth-value","display_name":"Truth value","score":0.4286026060581207},{"id":"https://openalex.org/keywords/partial-evaluation","display_name":"Partial evaluation","score":0.42832356691360474},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4092881381511688},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3159272074699402},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.29098835587501526},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.280346155166626},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.13481193780899048},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.09738048911094666}],"concepts":[{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.7520013451576233},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7199644446372986},{"id":"https://openalex.org/C182359184","wikidata":"https://www.wikidata.org/wiki/Q1756942","display_name":"Partial function","level":2,"score":0.7160665988922119},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5100034475326538},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5089190006256104},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.473993182182312},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4599570035934448},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.440615713596344},{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.4286026060581207},{"id":"https://openalex.org/C195701839","wikidata":"https://www.wikidata.org/wiki/Q4008398","display_name":"Partial evaluation","level":2,"score":0.42832356691360474},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4092881381511688},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3159272074699402},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29098835587501526},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.280346155166626},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.13481193780899048},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.09738048911094666},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2274487","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274487","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/1183743419","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183743419","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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.5}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W4861723","https://openalex.org/W6204907","https://openalex.org/W126568045","https://openalex.org/W592023824","https://openalex.org/W647911039","https://openalex.org/W914834656","https://openalex.org/W981129589","https://openalex.org/W1492008767","https://openalex.org/W1498523273","https://openalex.org/W1498831097","https://openalex.org/W1518290936","https://openalex.org/W1565996669","https://openalex.org/W1585676614","https://openalex.org/W1911653709","https://openalex.org/W1986402635","https://openalex.org/W1996404651","https://openalex.org/W2034676877","https://openalex.org/W2062506884","https://openalex.org/W2084797476","https://openalex.org/W2087011376","https://openalex.org/W2128057448","https://openalex.org/W2137033866","https://openalex.org/W2160331299","https://openalex.org/W2165434002","https://openalex.org/W2295902379","https://openalex.org/W2325825698","https://openalex.org/W2742270218","https://openalex.org/W3000593863","https://openalex.org/W3026313652","https://openalex.org/W3174395628","https://openalex.org/W3205594860","https://openalex.org/W4241775074","https://openalex.org/W4249355983","https://openalex.org/W4250282680","https://openalex.org/W4256124958","https://openalex.org/W4299731435"],"related_works":["https://openalex.org/W561052599","https://openalex.org/W2159591963","https://openalex.org/W184346136","https://openalex.org/W1511863848","https://openalex.org/W2107696941","https://openalex.org/W2143961378","https://openalex.org/W1556604985","https://openalex.org/W2189250964","https://openalex.org/W2963039416","https://openalex.org/W2184512187"],"abstract_inverted_index":{"Abstract":[0],"Church's":[1,28,100],"simple":[2],"theory":[3],"of":[4,9,27,40,92,99],"types":[5],"is":[6,44,69],"a":[7,25,61],"system":[8,29],"higher-order":[10],"logic":[11],"in":[12,22,32,79],"which":[13,33,43],"functions":[14,34,83],"are":[15],"assumed":[16],"to":[17,52,58,73,86,96],"be":[18,36,53],"total.":[19],"We":[20,65],"present":[21],"this":[23],"paper":[24],"version":[26],"called":[30],"PF":[31,41,68,80,93],"may":[35],"partial.":[37],"The":[38,76],"semantics":[39],",":[42],"based":[45],"on":[46],"Henkin's":[47],"general-models":[48],"semantics,":[49],"allows":[50],"terms":[51],"nondenoting":[54],"but":[55],"requires":[56],"formulas":[57],"always":[59],"denote":[60],"standard":[62],"truth":[63],"value.":[64],"prove":[66],"that":[67],"complete":[70],"with":[71],"respect":[72],"its":[74],"semantics.":[75],"reasoning":[77],"mechanism":[78],"for":[81],"partial":[82],"corresponds":[84],"closely":[85],"mathematical":[87],"practice,":[88],"and":[89],"the":[90,97],"formulation":[91],"adheres":[94],"tightly":[95],"framework":[98],"system.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
