{"id":"https://openalex.org/W4414570844","doi":"https://doi.org/10.1007/978-3-032-06085-3_21","title":"Justification Logic for\u00a0Intuitionistic Modal Logic","display_name":"Justification Logic for\u00a0Intuitionistic Modal Logic","publication_year":2025,"publication_date":"2025-09-25","ids":{"openalex":"https://openalex.org/W4414570844","doi":"https://doi.org/10.1007/978-3-032-06085-3_21"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-032-06085-3_21","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-06085-3_21","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-06085-3_21.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-06085-3_21.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045817513","display_name":"Sonia Marin","orcid":null},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Sonia Marin","raw_affiliation_strings":["School of Computer Science, University of Birmingham, Birmingham, UK"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Birmingham, Birmingham, UK","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5099137408","display_name":"Paaras Padhiar","orcid":null},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Paaras Padhiar","raw_affiliation_strings":["School of Computer Science, University of Birmingham, Birmingham, UK"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Birmingham, Birmingham, UK","institution_ids":["https://openalex.org/I79619799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045817513"],"corresponding_institution_ids":["https://openalex.org/I79619799"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.43594186,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"393","last_page":"413"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9962000250816345,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9961000084877014,"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/normal-modal-logic","display_name":"Normal modal logic","score":0.7940999865531921},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.7634999752044678},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.7063000202178955},{"id":"https://openalex.org/keywords/sequent","display_name":"Sequent","score":0.6733999848365784},{"id":"https://openalex.org/keywords/s5","display_name":"S5","score":0.5841000080108643},{"id":"https://openalex.org/keywords/accessibility-relation","display_name":"Accessibility relation","score":0.5519000291824341},{"id":"https://openalex.org/keywords/modal-\u03bc-calculus","display_name":"Modal \u03bc-calculus","score":0.5422999858856201},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5374000072479248},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5236999988555908}],"concepts":[{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.7940999865531921},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.7634999752044678},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.7063000202178955},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.6733999848365784},{"id":"https://openalex.org/C192609573","wikidata":"https://www.wikidata.org/wiki/Q7388341","display_name":"S5","level":5,"score":0.5841000080108643},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.5519000291824341},{"id":"https://openalex.org/C173125200","wikidata":"https://www.wikidata.org/wiki/Q5275729","display_name":"Modal \u03bc-calculus","level":5,"score":0.5422999858856201},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5374000072479248},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5236999988555908},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5231000185012817},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.5170000195503235},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.5026999711990356},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.48820000886917114},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.4602999985218048},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.44859999418258667},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.42739999294281006},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.41290000081062317},{"id":"https://openalex.org/C111404639","wikidata":"https://www.wikidata.org/wiki/Q376166","display_name":"Cut-elimination theorem","level":4,"score":0.40290001034736633},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39160001277923584},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.33390000462532043},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33250001072883606},{"id":"https://openalex.org/C78344899","wikidata":"https://www.wikidata.org/wiki/Q638442","display_name":"Modal operator","level":4,"score":0.32839998602867126},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30720001459121704},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C6489637","wikidata":"https://www.wikidata.org/wiki/Q7250002","display_name":"Proof calculus","level":3,"score":0.26910001039505005},{"id":"https://openalex.org/C171482190","wikidata":"https://www.wikidata.org/wiki/Q3257974","display_name":"Minimal logic","level":5,"score":0.26589998602867126},{"id":"https://openalex.org/C60048249","wikidata":"https://www.wikidata.org/wiki/Q37437","display_name":"Syntax","level":2,"score":0.2621999979019165}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-032-06085-3_21","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-06085-3_21","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-06085-3_21.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/5efb6dc8-5a56-4b9c-aef9-a289b4f0a984","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/5efb6dc8-5a56-4b9c-aef9-a289b4f0a984","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"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":"Marin, S & Padhiar, P 2025, Justification Logic for Intuitionistic Modal Logic. in G L Pozzato & T Uustalu (eds), Automated Reasoning with Analytic Tableaux and Related Methods : 34th International Conference, TABLEAUX 2025, Reykjavik, Iceland, September 27\u201329, 2025, Proceedings. Lecture Notes in Computer Science, vol. 15980, Springer, pp. 393-413, 34th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2025, Reykjavik, Iceland, 27/07/25. https://doi.org/10.1007/978-3-032-06085-3_21","raw_type":"contributionToPeriodical"}],"best_oa_location":{"id":"doi:10.1007/978-3-032-06085-3_21","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-06085-3_21","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-06085-3_21.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414570844.pdf","grobid_xml":"https://content.openalex.org/works/W4414570844.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W49329176","https://openalex.org/W101915042","https://openalex.org/W207654131","https://openalex.org/W570944246","https://openalex.org/W1561374751","https://openalex.org/W1678412398","https://openalex.org/W1763969474","https://openalex.org/W1966647830","https://openalex.org/W1969042337","https://openalex.org/W1996723544","https://openalex.org/W2015385255","https://openalex.org/W2018205748","https://openalex.org/W2031962352","https://openalex.org/W2043468053","https://openalex.org/W2045237008","https://openalex.org/W2050519161","https://openalex.org/W2074011039","https://openalex.org/W2083186217","https://openalex.org/W2093881948","https://openalex.org/W2187936207","https://openalex.org/W2224511541","https://openalex.org/W2247407447","https://openalex.org/W2772042761","https://openalex.org/W2961141088","https://openalex.org/W3098895866","https://openalex.org/W4211092209","https://openalex.org/W4386723704","https://openalex.org/W4401307137","https://openalex.org/W4414693961"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Justification":[1],"logic":[2,64,97,135],"is":[3],"an":[4,138],"explication":[5],"of":[6,87,124,132,140],"modal":[7,31,43,63,96,134,157],"logic:":[8],"boxes":[9,45],"are":[10,48],"replaced":[11],"with":[12,106,144],"proof":[13,27,125],"terms":[14,80,126],"formally":[15],"through":[16],"realisation":[17,147],"theorems.":[18],"This":[19],"can":[20],"be":[21],"achieved":[22],"syntactically":[23],"using":[24,34,149],"a":[25,30,58,91,145,150],"cut-free":[26,151],"system":[28,154],"for":[29,155],"logic,":[32,44],"e.g.,":[33],"sequent,":[35],"hypersequent,":[36],"or":[37],"nested":[38,152],"sequent":[39,153],"calculi.":[40],"In":[41],"constructive":[42,62],"and":[46,50,77,89,103,113,136],"diamonds":[47,75],"decoupled":[49],"not":[51],"De":[52],"Morgan":[53],"dual.":[54],"Previous":[55],"work":[56,88],"provides":[57],"justification":[59,92,142],"counterpart":[60,93],"to":[61,94,127],"$$\\textsf{CK}$$":[65],"<mml:math":[66,99,109,115],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[67,100,110,116],"<mml:mi>CK</mml:mi>":[68],"</mml:math>":[69,102,112,118],"(and":[70],"some":[71],"extensions)":[72],"by":[73],"making":[74],"explicit":[76],"introducing":[78],"new":[79],"called":[81],"satisfiers.":[82],"We":[83,120],"continue":[84],"this":[85],"line":[86],"provide":[90,137],"intuitionistic":[95,133,156],"$$\\textsf{IK}$$":[98],"<mml:mi>IK</mml:mi>":[101],"its":[104],"extensions":[105],"the":[107,122,129],"$$\\textsf{t}$$":[108],"<mml:mi>t</mml:mi>":[111],"$$\\textsf{4}$$":[114],"<mml:mn>4</mml:mn>":[117],"axioms.":[119],"extend":[121],"syntax":[123],"accommodate":[128],"additional":[130],"axioms":[131],"axiomatisation":[139],"these":[141],"logics":[143],"syntactic":[146],"procedure":[148],"logic.":[158]},"counts_by_year":[],"updated_date":"2026-03-15T09:29:46.208133","created_date":"2025-10-10T00:00:00"}
