{"id":"https://openalex.org/W1998289751","doi":"https://doi.org/10.1215/00294527-2009-011","title":"Proof-finding Algorithms for Classical and Subclassical Propositional Logics","display_name":"Proof-finding Algorithms for Classical and Subclassical Propositional Logics","publication_year":2009,"publication_date":"2009-07-01","ids":{"openalex":"https://openalex.org/W1998289751","doi":"https://doi.org/10.1215/00294527-2009-011","mag":"1998289751"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-2009-011","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2009-011","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-3/Proof-finding-Algorithms-for-Classical-and-Subclassical-Propositional-Logics/10.1215/00294527-2009-011.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-3/Proof-finding-Algorithms-for-Classical-and-Subclassical-Propositional-Logics/10.1215/00294527-2009-011.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038043998","display_name":"M. W. Bunder","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"M. W. Bunder","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5084718152","display_name":"Ramzy Master Rizkalla","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. M. Rizkalla","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038043998"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08326671,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"50","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9994999766349792,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9980000257492065,"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":0.7643152475357056},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.7155942320823669},{"id":"https://openalex.org/keywords/propositional-variable","display_name":"Propositional variable","score":0.6726784706115723},{"id":"https://openalex.org/keywords/lambda-calculus","display_name":"Lambda calculus","score":0.5899209976196289},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.5769156217575073},{"id":"https://openalex.org/keywords/curry\u2013howard-correspondence","display_name":"Curry\u2013Howard correspondence","score":0.5752911567687988},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5490307807922363},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5239741206169128},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5150834918022156},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5029534697532654},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4511024057865143},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.44818899035453796},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.43088364601135254},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.42965930700302124},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4176212251186371},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.4169897735118866},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.360524445772171},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2552286982536316},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.06912657618522644}],"concepts":[{"id":"https://openalex.org/C79678938","wikidata":"https://www.wikidata.org/wiki/Q1481571","display_name":"Combinatory logic","level":2,"score":0.7643152475357056},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.7155942320823669},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.6726784706115723},{"id":"https://openalex.org/C135790938","wikidata":"https://www.wikidata.org/wiki/Q242028","display_name":"Lambda calculus","level":2,"score":0.5899209976196289},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.5769156217575073},{"id":"https://openalex.org/C85343465","wikidata":"https://www.wikidata.org/wiki/Q975734","display_name":"Curry\u2013Howard correspondence","level":3,"score":0.5752911567687988},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5490307807922363},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5239741206169128},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5150834918022156},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5029534697532654},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4511024057865143},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.44818899035453796},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.43088364601135254},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.42965930700302124},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4176212251186371},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.4169897735118866},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.360524445772171},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2552286982536316},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.06912657618522644},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1215/00294527-2009-011","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2009-011","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-3/Proof-finding-Algorithms-for-Classical-and-Subclassical-Propositional-Logics/10.1215/00294527-2009-011.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:ro.uow.edu.au:era-2818","is_oa":false,"landing_page_url":"https://ro.uow.edu.au/cgi/viewcontent.cgi?article=2818&context=era","pdf_url":null,"source":{"id":"https://openalex.org/S4306400510","display_name":"Research Online (University of Wollongong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I204824540","host_organization_name":"University of Wollongong","host_organization_lineage":["https://openalex.org/I204824540"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ERA - University of Wollongong (restricted)","raw_type":"article"},{"id":"pmh:oai:ro.uow.edu.au:infopapers-10580","is_oa":false,"landing_page_url":"https://ro.uow.edu.au/infopapers/3244","pdf_url":null,"source":{"id":"https://openalex.org/S4306400510","display_name":"Research Online (University of Wollongong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I204824540","host_organization_name":"University of Wollongong","host_organization_lineage":["https://openalex.org/I204824540"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty of Informatics - Papers (Archive)","raw_type":"article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1257862038","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1257862038","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":{"id":"doi:10.1215/00294527-2009-011","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2009-011","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-3/Proof-finding-Algorithms-for-Classical-and-Subclassical-Propositional-Logics/10.1215/00294527-2009-011.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1998289751.pdf","grobid_xml":"https://content.openalex.org/works/W1998289751.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W179909826","https://openalex.org/W1528534845","https://openalex.org/W1996701064","https://openalex.org/W2030827886","https://openalex.org/W2037135838","https://openalex.org/W2045304669","https://openalex.org/W2088508256","https://openalex.org/W2134870220"],"related_works":["https://openalex.org/W44725458","https://openalex.org/W164671196","https://openalex.org/W2811159399","https://openalex.org/W349188499","https://openalex.org/W2954585109","https://openalex.org/W2612830858","https://openalex.org/W1571094673","https://openalex.org/W1998289751","https://openalex.org/W2740609775","https://openalex.org/W2183401507"],"abstract_inverted_index":{"The":[0,28],"formulas-as-types":[1],"isomorphism":[2],"tells":[3],"us":[4],"that":[5],"every":[6],"proof":[7],"and":[8,25,48],"theorem,":[9],"in":[10,82],"the":[11,57,67,70],"intuitionistic":[12],"implicational":[13],"logic":[14,95],"H":[15,46],"\u2192":[16,47],",":[17],"corresponds":[18],"to":[19,91,99],"a":[20,35,61],"lambda":[21,36],"term":[22,37],"or":[23],"combinator":[24],"its":[26,52,100],"type.":[27],"algorithms":[29],"of":[30,41,45,49,51,69,75,77],"Bunder":[31],"very":[32],"efficiently":[33],"find":[34],"inhabitant,":[38],"if":[39],"any,":[40],"any":[42],"given":[43],"type":[44],"many":[50],"subsystems.":[53,102],"In":[54,84],"most":[55],"cases":[56],"search":[58],"procedure":[59],"has":[60,105],"simple":[62],"bound":[63],"based":[64],"roughly":[65],"on":[66],"length":[68],"formula":[71],"involved.":[72],"Computer":[73],"implementations":[74],"some":[76],"these":[78,89],"procedures":[79],"were":[80],"done":[81],"Dekker.":[83],"this":[85],"paper":[86],"we":[87],"extend":[88],"methods":[90],"full":[92],"classical":[93],"propositional":[94],"as":[96,98],"well":[97],"various":[101],"This":[103],"extension":[104],"partly":[106],"been":[107],"implemented":[108],"by":[109],"Oostdijk.":[110]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}