{"id":"https://openalex.org/W2769039174","doi":"https://doi.org/10.1017/s1755020319000297","title":"MECHANIZING <i>PRINCIPIA LOGICO-METAPHYSICA</i> IN FUNCTIONAL TYPE-THEORY","display_name":"MECHANIZING <i>PRINCIPIA LOGICO-METAPHYSICA</i> IN FUNCTIONAL TYPE-THEORY","publication_year":2019,"publication_date":"2019-07-12","ids":{"openalex":"https://openalex.org/W2769039174","doi":"https://doi.org/10.1017/s1755020319000297","mag":"2769039174"},"language":"en","primary_location":{"id":"doi:10.1017/s1755020319000297","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020319000297","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"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":"The Review of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1711.06542","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"DANIEL KIRCHNER","orcid":null},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"DANIEL KIRCHNER","raw_affiliation_strings":["Fachbereich Mathematik und Informatik, Freie Universit\u00e4t Berlin"],"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Informatik, Freie Universit\u00e4t Berlin","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":null,"display_name":"CHRISTOPH BENZM\u00dcLLER","orcid":null},"institutions":[{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]}],"countries":["LU"],"is_corresponding":true,"raw_author_name":"CHRISTOPH BENZM\u00dcLLER","raw_affiliation_strings":["Fachbereich Mathematik und Informatik, Freie Universit\u00e4t Berlin and Computer Science and Communications, University of Luxembourg"],"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Informatik, Freie Universit\u00e4t Berlin and Computer Science and Communications, University of Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]},{"author_position":"last","author":{"id":null,"display_name":"EDWARD N. ZALTA","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"EDWARD N. ZALTA","raw_affiliation_strings":["Center for the Study of Language and Information, Stanford University"],"affiliations":[{"raw_affiliation_string":"Center for the Study of Language and Information, Stanford University","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I186903577","https://openalex.org/I75951250","https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":0.5781,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.74302458,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"13","issue":"1","first_page":"206","last_page":"218"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.439300000667572,"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":0.439300000667572,"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/T10258","display_name":"Philosophy and Theoretical Science","score":0.3573000133037567,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.09849999845027924,"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/embedding","display_name":"Embedding","score":0.559499979019165},{"id":"https://openalex.org/keywords/metatheory","display_name":"Metatheory","score":0.46790000796318054},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.4586000144481659},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.44670000672340393},{"id":"https://openalex.org/keywords/dependency","display_name":"Dependency (UML)","score":0.3765999972820282},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.37540000677108765},{"id":"https://openalex.org/keywords/domain-theory","display_name":"Domain theory","score":0.3700000047683716},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.36959999799728394},{"id":"https://openalex.org/keywords/foundation","display_name":"Foundation (evidence)","score":0.35740000009536743},{"id":"https://openalex.org/keywords/comprehension","display_name":"Comprehension","score":0.3434000015258789}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5648999810218811},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.559499979019165},{"id":"https://openalex.org/C39387531","wikidata":"https://www.wikidata.org/wiki/Q1096708","display_name":"Metatheory","level":2,"score":0.46790000796318054},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.45980000495910645},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.4586000144481659},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.44670000672340393},{"id":"https://openalex.org/C19768560","wikidata":"https://www.wikidata.org/wiki/Q320727","display_name":"Dependency (UML)","level":2,"score":0.3765999972820282},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.37540000677108765},{"id":"https://openalex.org/C29585364","wikidata":"https://www.wikidata.org/wiki/Q1079166","display_name":"Domain theory","level":2,"score":0.3700000047683716},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.36959999799728394},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36010000109672546},{"id":"https://openalex.org/C2780966255","wikidata":"https://www.wikidata.org/wiki/Q5474306","display_name":"Foundation (evidence)","level":2,"score":0.35740000009536743},{"id":"https://openalex.org/C511192102","wikidata":"https://www.wikidata.org/wiki/Q5156948","display_name":"Comprehension","level":2,"score":0.3434000015258789},{"id":"https://openalex.org/C32241873","wikidata":"https://www.wikidata.org/wiki/Q236975","display_name":"Classical logic","level":2,"score":0.33550000190734863},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C206588197","wikidata":"https://www.wikidata.org/wiki/Q846574","display_name":"Reuse","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3133000135421753},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30979999899864197},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.30709999799728394},{"id":"https://openalex.org/C171268870","wikidata":"https://www.wikidata.org/wiki/Q1486676","display_name":"GRASP","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C105056347","wikidata":"https://www.wikidata.org/wiki/Q3239681","display_name":"Scientific theory","level":2,"score":0.305400013923645},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C195818886","wikidata":"https://www.wikidata.org/wiki/Q5421724","display_name":"Expressive power","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C106624574","wikidata":"https://www.wikidata.org/wiki/Q5270387","display_name":"Diagrammatic reasoning","level":2,"score":0.2980000078678131},{"id":"https://openalex.org/C182744844","wikidata":"https://www.wikidata.org/wiki/Q35277","display_name":"Metaphysics","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C20693621","wikidata":"https://www.wikidata.org/wiki/Q6667502","display_name":"Logical framework","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2870999872684479},{"id":"https://openalex.org/C101874905","wikidata":"https://www.wikidata.org/wiki/Q2476757","display_name":"Philosophy of logic","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C25810664","wikidata":"https://www.wikidata.org/wiki/Q44325","display_name":"Ontology","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C2776085556","wikidata":"https://www.wikidata.org/wiki/Q183361","display_name":"Chen","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C134752490","wikidata":"https://www.wikidata.org/wiki/Q374182","display_name":"Logical consequence","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s1755020319000297","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020319000297","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"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":"The Review of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1711.06542","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.06542","pdf_url":"https://arxiv.org/pdf/1711.06542","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:orbilu.uni.lu:10993/33700","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1711.06542","pdf_url":null,"source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:orbilu.uni.lu:10993/40542","is_oa":true,"landing_page_url":"http://orbilu.uni.lu/handle/10993/40542","pdf_url":null,"source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Review of Symbolic Logic, 1-13 (2019-07-12)","raw_type":"peer reviewed"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1711.06542","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.06542","pdf_url":"https://arxiv.org/pdf/1711.06542","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1989156455","https://openalex.org/W1996404651","https://openalex.org/W2030002668","https://openalex.org/W2104838937","https://openalex.org/W2326349045","https://openalex.org/W2901339989","https://openalex.org/W4252907082","https://openalex.org/W6745621531"],"related_works":[],"abstract_inverted_index":{"Abstract":[0,20],"Principia":[1],"Logico-Metaphysica":[2],"contains":[3],"a":[4,16,24,71,76,105,144,163,210,228],"foundational":[5],"logical":[6],"theory":[7,26,220,224],"for":[8,100,143,194,230],"metaphysics,":[9],"mathematics,":[10],"and":[11,40,56,78,107,114,139,196,201,232],"the":[12,60,86,121,128,133,214],"sciences.":[13],"It":[14],"includes":[15],"canonical":[17],"development":[18],"of":[19,30,88,124,135,147,166,216],"Object":[21],"Theory":[22],"[AOT],":[23],"metaphysical":[25],"(inspired":[27],"by":[28,34,119,162,173],"ideas":[29],"Ernst":[31],"Mally,":[32],"formalized":[33],"Zalta)":[35],"that":[36],"distinguishes":[37],"between":[38],"ordinary":[39],"abstract":[41],"objects.":[42],"This":[43,102,181],"article":[44],"reports":[45],"on":[46,213],"recent":[47],"work":[48],"in":[49,59,83,127,150,177],"which":[50],"AOT":[51,84],"has":[52],"been":[53],"successfully":[54],"represented":[55],"partly":[57],"automated":[58],"proof":[61,189],"assistant":[62],"system":[63],"Isabelle/HOL.":[64],"Initial":[65],"experiments":[66],"within":[67],"this":[68],"framework":[69],"reveal":[70],"crucial":[72],"but":[73],"overlooked":[74],"fact:":[75],"deeply-rooted":[77],"known":[79],"paradox":[80],"is":[81,91,117,132],"reintroduced":[82],"when":[85],"logic":[87,231],"complex":[89,125],"terms":[90,126],"simply":[92],"adjoined":[93],"to":[94,170,185],"AOT\u2019s":[95],"specially":[96],"formulated":[97],"comprehension":[98],"principle":[99],"relations.":[101],"result":[103],"constitutes":[104],"new":[106,145],"important":[108],"paradox,":[109],"given":[110],"how":[111],"much":[112],"expressive":[113],"analytic":[115],"power":[116],"contributed":[118],"having":[120],"two":[122],"kinds":[123],"system.":[129],"Its":[130],"discovery":[131],"highlight":[134],"our":[136],"joint":[137],"project":[138],"provides":[140],"strong":[141],"evidence":[142],"kind":[146],"scientific":[148],"practice":[149],"philosophy,":[151],"namely,":[152],"computational":[153],"metaphysics":[154],".":[155],"Our":[156,206],"results":[157,207],"were":[158],"made":[159],"technically":[160],"possible":[161],"suitable":[164],"adaptation":[165],"Benzm\u00fcller\u2019s":[167],"metalogical":[168],"approach":[169,182],"universal":[171],"reasoning":[172],"semantically":[174],"embedding":[175],"theories":[176,202],"classical":[178],"higher-order":[179,188],"logic.":[180],"enables":[183],"one":[184],"reuse":[186],"state-of-the-art":[187],"assistants,":[190],"such":[191,203],"as":[192,204,227],"Isabelle/HOL,":[193],"mechanizing":[195],"experimentally":[197],"exploring":[198],"challenging":[199],"logics":[200],"AOT.":[205],"also":[208],"provide":[209],"fresh":[211],"perspective":[212],"question":[215],"whether":[217],"relational":[218],"type":[219,223],"or":[221],"functional":[222],"better":[225],"serves":[226],"foundation":[229],"metaphysics.":[233]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2017-12-04T00:00:00"}