{"id":"https://openalex.org/W1983240156","doi":"https://doi.org/10.1007/s11225-006-9009-6","title":"Pure Extensions, Proof Rules, and Hybrid Axiomatics","display_name":"Pure Extensions, Proof Rules, and Hybrid Axiomatics","publication_year":2006,"publication_date":"2006-11-08","ids":{"openalex":"https://openalex.org/W1983240156","doi":"https://doi.org/10.1007/s11225-006-9009-6","mag":"1983240156"},"language":"en","primary_location":{"id":"doi:10.1007/s11225-006-9009-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11225-006-9009-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11225-006-9009-6.pdf","source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studia Logica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s11225-006-9009-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044128824","display_name":"Patrick Blackburn","orcid":"https://orcid.org/0000-0001-9345-552X"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"P. Blackburn","raw_affiliation_strings":["INRIA Lorraine, Villers les Nancy Cedex, France","Inria-Lorraine#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA Lorraine, Villers les Nancy Cedex, France","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"Inria-Lorraine#TAB#","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080220262","display_name":"Balder ten Cate","orcid":"https://orcid.org/0000-0002-2538-5846"},"institutions":[{"id":"https://openalex.org/I55106644","display_name":"Amsterdam University of Applied Sciences","ror":"https://ror.org/00y2z2s03","country_code":"NL","type":"education","lineage":["https://openalex.org/I55106644"]},{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]},{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"B. ten Cate","raw_affiliation_strings":["ISLA, Informatics Institute, Universiteit van Amsterdam , SJ Amsterdam, The Netherlands","Universiteit van Amsterdam;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ISLA, Informatics Institute, Universiteit van Amsterdam , SJ Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I55106644","https://openalex.org/I865915315"]},{"raw_affiliation_string":"Universiteit van Amsterdam;","institution_ids":["https://openalex.org/I887064364"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5044128824","https://openalex.org/A5080220262"],"corresponding_institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I55106644","https://openalex.org/I865915315","https://openalex.org/I887064364"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":8.407,"has_fulltext":true,"cited_by_count":91,"citation_normalized_percentile":{"value":0.97118244,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"84","issue":"2","first_page":"277","last_page":"322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","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/T11010","display_name":"Logic, Reasoning, and Knowledge","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/T11727","display_name":"Advanced Algebra and Logic","score":0.9977999925613403,"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"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9976999759674072,"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/kripke-semantics","display_name":"Kripke semantics","score":0.609991192817688},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5825979709625244},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.5453192591667175},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.5444047451019287},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.44637876749038696},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.4327927529811859},{"id":"https://openalex.org/keywords/fragment","display_name":"Fragment (logic)","score":0.4212181568145752},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.4133393168449402},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.386710524559021},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3340463638305664},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.3228036165237427},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.30710816383361816},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.27183330059051514},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2477765679359436},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.14265531301498413}],"concepts":[{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.609991192817688},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5825979709625244},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.5453192591667175},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.5444047451019287},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.44637876749038696},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.4327927529811859},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.4212181568145752},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.4133393168449402},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.386710524559021},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3340463638305664},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.3228036165237427},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.30710816383361816},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.27183330059051514},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2477765679359436},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.14265531301498413},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1007/s11225-006-9009-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11225-006-9009-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11225-006-9009-6.pdf","source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studia Logica","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.100.7583","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.100.7583","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.loria.fr/~blackbur/papers/axiomsAIML.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.125.3762","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.125.3762","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://staff.science.uva.nl/~bcate/papers/pureaxioms-aiml.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.141.1270","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.141.1270","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://staff.science.uva.nl/~bcate/papers/sl-axiomatics.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:inria-00119855v1","is_oa":false,"landing_page_url":"https://inria.hal.science/inria-00119855","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Studia Logica, 2006, 84 (2), pp.277-322. &#x27E8;10.1007/s11225-006-9009-6&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:dare.uva.nl:publications/546c624b-f788-4e75-9165-27e6d35bb8bd","is_oa":false,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/pure-extensions-proof-rules-and-hybrid-axiomatics(546c624b-f788-4e75-9165-27e6d35bb8bd).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Blackburn, P & ten Cate, B D 2004, Pure extensions, proof rules and hybrid axiomatics. in R Schmidt & I Pratt-Hartmann (eds), Preliminary proceedings of Advances in Modal Logic 2004. Manchester, pp. 16-29, Advances in Modal Logic 2004, 9/09/04.","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:dare.uva.nl:publications/e6a56a74-ce51-42e8-a766-5be7adf6df07","is_oa":false,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/pure-extensions-proof-rules-and-hybrid-axiomatics(e6a56a74-ce51-42e8-a766-5be7adf6df07).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Blackburn, P & ten Cate, B D 2006, 'Pure extensions, proof rules, and hybrid axiomatics', Studia Logica, vol. 84, pp. 277-322.","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:uvapub:oai:dare.uva.nl:publications/546c624b-f788-4e75-9165-27e6d35bb8bd","is_oa":false,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/pure-extensions-proof-rules-and-hybrid-axiomatics(546c624b-f788-4e75-9165-27e6d35bb8bd).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Preliminary proceedings of Advances in Modal Logic 2004, 16 - 29","raw_type":"info:eu-repo/semantics/conferencepaper"},{"id":"pmh:uvapub:oai:dare.uva.nl:publications/e6a56a74-ce51-42e8-a766-5be7adf6df07","is_oa":false,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/pure-extensions-proof-rules-and-hybrid-axiomatics(e6a56a74-ce51-42e8-a766-5be7adf6df07).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Studia Logica, 84, 277 - 322. Springer Netherlands","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s11225-006-9009-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11225-006-9009-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11225-006-9009-6.pdf","source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studia Logica","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.6600000262260437}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1983240156.pdf","grobid_xml":"https://content.openalex.org/works/W1983240156.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W5642659","https://openalex.org/W78460491","https://openalex.org/W829324876","https://openalex.org/W1480314582","https://openalex.org/W1489300317","https://openalex.org/W1489496002","https://openalex.org/W1522945997","https://openalex.org/W1527588453","https://openalex.org/W1527720545","https://openalex.org/W1555450189","https://openalex.org/W1689987508","https://openalex.org/W1869682152","https://openalex.org/W1919847619","https://openalex.org/W1928206718","https://openalex.org/W1969118410","https://openalex.org/W1974866079","https://openalex.org/W1976307763","https://openalex.org/W1981936535","https://openalex.org/W1987374077","https://openalex.org/W1991153667","https://openalex.org/W1991402517","https://openalex.org/W2018462672","https://openalex.org/W2047294512","https://openalex.org/W2061003582","https://openalex.org/W2064773636","https://openalex.org/W2065265012","https://openalex.org/W2068458083","https://openalex.org/W2075277371","https://openalex.org/W2076805456","https://openalex.org/W2088302563","https://openalex.org/W2092576830","https://openalex.org/W2101263826","https://openalex.org/W2116784584","https://openalex.org/W2122473064","https://openalex.org/W2133700101","https://openalex.org/W2153417525","https://openalex.org/W2154199572","https://openalex.org/W2155581733","https://openalex.org/W2161004731","https://openalex.org/W2170352409","https://openalex.org/W2225187755","https://openalex.org/W2610670723","https://openalex.org/W3144889436","https://openalex.org/W4211144022","https://openalex.org/W4239399053","https://openalex.org/W4255199623","https://openalex.org/W4256000740","https://openalex.org/W6662420862","https://openalex.org/W6793045953"],"related_works":["https://openalex.org/W2077061463","https://openalex.org/W3111905456","https://openalex.org/W2064387576","https://openalex.org/W2881541399","https://openalex.org/W1599533611","https://openalex.org/W2101793126","https://openalex.org/W2974949998","https://openalex.org/W2271944696","https://openalex.org/W2062728934","https://openalex.org/W2038216920"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
