{"id":"https://openalex.org/W2163197731","doi":"https://doi.org/10.2307/2275545","title":"On the complexity of propositional quantification in intuitionistic logic","display_name":"On the complexity of propositional quantification in intuitionistic logic","publication_year":1997,"publication_date":"1997-06-01","ids":{"openalex":"https://openalex.org/W2163197731","doi":"https://doi.org/10.2307/2275545","mag":"2163197731"},"language":"en","primary_location":{"id":"doi:10.2307/2275545","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2275545","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3C0D1F4C5EED1B6480B24F5F93CDE98D/S0022481200016340a.pdf/div-class-title-on-the-complexity-of-propositional-quantification-in-intuitionistic-logic-div.pdf","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":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3C0D1F4C5EED1B6480B24F5F93CDE98D/S0022481200016340a.pdf/div-class-title-on-the-complexity-of-propositional-quantification-in-intuitionistic-logic-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042962543","display_name":"Philip Kremer","orcid":null},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Philip Kremer","raw_affiliation_strings":["Department of Philosophy, Yale University, P.O. Box 208306, New Haven, CT 06520-8306, USA, E-mail:","DEPARTMENT OF PHILOSOPHY YALE UNIVERSITY P.O. BOX 208306 NEW HAVEN, CT 06520-8306, USA"],"affiliations":[{"raw_affiliation_string":"Department of Philosophy, Yale University, P.O. Box 208306, New Haven, CT 06520-8306, USA, E-mail:","institution_ids":["https://openalex.org/I32971472"]},{"raw_affiliation_string":"DEPARTMENT OF PHILOSOPHY YALE UNIVERSITY P.O. BOX 208306 NEW HAVEN, CT 06520-8306, USA","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5042962543"],"corresponding_institution_ids":["https://openalex.org/I32971472"],"apc_list":null,"apc_paid":null,"fwci":3.6226,"has_fulltext":true,"cited_by_count":44,"citation_normalized_percentile":{"value":0.93514604,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"62","issue":"2","first_page":"529","last_page":"544"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9973999857902527,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9973999857902527,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9905999898910522,"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":0.989300012588501,"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/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.8743389248847961},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.7963769435882568},{"id":"https://openalex.org/keywords/propositional-variable","display_name":"Propositional variable","score":0.7207035422325134},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.6664181351661682},{"id":"https://openalex.org/keywords/kripke-semantics","display_name":"Kripke semantics","score":0.6020256876945496},{"id":"https://openalex.org/keywords/autoepistemic-logic","display_name":"Autoepistemic logic","score":0.5364805459976196},{"id":"https://openalex.org/keywords/zeroth-order-logic","display_name":"Zeroth-order logic","score":0.5241482257843018},{"id":"https://openalex.org/keywords/dynamic-logic","display_name":"Dynamic logic (digital electronics)","score":0.5164594650268555},{"id":"https://openalex.org/keywords/many-valued-logic","display_name":"Many-valued logic","score":0.48049628734588623},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47610458731651306},{"id":"https://openalex.org/keywords/minimal-logic","display_name":"Minimal logic","score":0.4597935378551483},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.45558980107307434},{"id":"https://openalex.org/keywords/s5","display_name":"S5","score":0.42123839259147644},{"id":"https://openalex.org/keywords/well-formed-formula","display_name":"Well-formed formula","score":0.4206641912460327},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41798219084739685},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.3854941725730896},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.3362712264060974},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.31282946467399597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30329132080078125},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.16338664293289185},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.14805585145950317},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07171860337257385}],"concepts":[{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.8743389248847961},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.7963769435882568},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.7207035422325134},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6664181351661682},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.6020256876945496},{"id":"https://openalex.org/C3845977","wikidata":"https://www.wikidata.org/wiki/Q4826262","display_name":"Autoepistemic logic","level":4,"score":0.5364805459976196},{"id":"https://openalex.org/C110039528","wikidata":"https://www.wikidata.org/wiki/Q8069651","display_name":"Zeroth-order logic","level":4,"score":0.5241482257843018},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.5164594650268555},{"id":"https://openalex.org/C150889026","wikidata":"https://www.wikidata.org/wiki/Q185502","display_name":"Many-valued logic","level":3,"score":0.48049628734588623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47610458731651306},{"id":"https://openalex.org/C171482190","wikidata":"https://www.wikidata.org/wiki/Q3257974","display_name":"Minimal logic","level":5,"score":0.4597935378551483},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.45558980107307434},{"id":"https://openalex.org/C192609573","wikidata":"https://www.wikidata.org/wiki/Q7388341","display_name":"S5","level":5,"score":0.42123839259147644},{"id":"https://openalex.org/C191222856","wikidata":"https://www.wikidata.org/wiki/Q655328","display_name":"Well-formed formula","level":5,"score":0.4206641912460327},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41798219084739685},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.3854941725730896},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.3362712264060974},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.31282946467399597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30329132080078125},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.16338664293289185},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.14805585145950317},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07171860337257385},{"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/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C172385210","wikidata":"https://www.wikidata.org/wiki/Q5339","display_name":"Transistor","level":3,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"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":4,"locations":[{"id":"doi:10.2307/2275545","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2275545","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3C0D1F4C5EED1B6480B24F5F93CDE98D/S0022481200016340a.pdf/div-class-title-on-the-complexity-of-propositional-quantification-in-intuitionistic-logic-div.pdf","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:utoronto.scholaris.ca:1807/90705","is_oa":true,"landing_page_url":"http://hdl.handle.net/1807/90705","pdf_url":"https://utoronto.scholaris.ca/bitstreams/6fc52e4e-298d-4364-9fc9-b363e81c66d9/download","source":{"id":"https://openalex.org/S7407055458","display_name":"TSpace","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Article Post-Print"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183745241","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745241","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.405.2698","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.405.2698","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://individual.utoronto.ca/philipkremer/onlinepapers/propquanint.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.2307/2275545","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2275545","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3C0D1F4C5EED1B6480B24F5F93CDE98D/S0022481200016340a.pdf/div-class-title-on-the-complexity-of-propositional-quantification-in-intuitionistic-logic-div.pdf","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"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4099999964237213,"display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334617","display_name":"Social Sciences and Humanities Research Council of Canada","ror":"https://ror.org/04j5jqy92"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2163197731.pdf","grobid_xml":"https://content.openalex.org/works/W2163197731.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1489060978","https://openalex.org/W1508227203","https://openalex.org/W1699512023","https://openalex.org/W1994211257","https://openalex.org/W1995421582","https://openalex.org/W2074092244","https://openalex.org/W2074944668","https://openalex.org/W2107589331","https://openalex.org/W2127394739","https://openalex.org/W2160331299","https://openalex.org/W2551720480","https://openalex.org/W2592837392","https://openalex.org/W4213130966","https://openalex.org/W4241241546"],"related_works":["https://openalex.org/W1558962892","https://openalex.org/W2064387576","https://openalex.org/W2352549085","https://openalex.org/W2754467536","https://openalex.org/W2055558461","https://openalex.org/W1500877097","https://openalex.org/W2156897951","https://openalex.org/W1785615301","https://openalex.org/W2009938424","https://openalex.org/W4386690957"],"abstract_inverted_index":{"Abstract":[0],"We":[1,22],"define":[2],"a":[3,12],"propositionally":[4],"quantified":[5],"intuitionistic":[6,20,43],"logic":[7],"H":[8,26,38],"\u03c0":[9,27,39,50,53,56,59,62,65,69],"+":[10,28,40,66,70],"by":[11,73],"natural":[13],"extension":[14],"of":[15,45],"Kripke's":[16],"semantics":[17],"for":[18],"propositional":[19],"logic.":[21,37],"then":[23],"show":[24],"that":[25],"is":[29,41],"recursively":[30],"isomorphic":[31],"to":[32],"full":[33],"second":[34],"order":[35],"classical":[36],"the":[42,46],"analogue":[44],"modal":[47],"systems":[48],"S5":[49],"+,":[51,54,57,60,63],"S4":[52],"S4.2":[55],"K4":[58],"T":[61],"K":[64],"and":[67],"B":[68],",":[71],"studied":[72],"Fine.":[74]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}