{"id":"https://openalex.org/W4414570856","doi":"https://doi.org/10.1007/978-3-032-06085-3_18","title":"Forward Proof Search for\u00a0Intuitionistic Multimodal K Logics","display_name":"Forward Proof Search for\u00a0Intuitionistic Multimodal K Logics","publication_year":2025,"publication_date":"2025-09-25","ids":{"openalex":"https://openalex.org/W4414570856","doi":"https://doi.org/10.1007/978-3-032-06085-3_18"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-032-06085-3_18","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-06085-3_18","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-06085-3_18.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_18.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058385346","display_name":"Niels Voorneveld","orcid":"https://orcid.org/0000-0001-6650-3493"},"institutions":[{"id":"https://openalex.org/I4210160054","display_name":"Cybernetica (Estonia)","ror":"https://ror.org/054gqc795","country_code":"EE","type":"company","lineage":["https://openalex.org/I4210160054"]}],"countries":["EE"],"is_corresponding":true,"raw_author_name":"Niels Voorneveld","raw_affiliation_strings":["Cybernetica AS, Tallinn, Estonia"],"affiliations":[{"raw_affiliation_string":"Cybernetica AS, Tallinn, Estonia","institution_ids":["https://openalex.org/I4210160054"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058385346"],"corresponding_institution_ids":["https://openalex.org/I4210160054"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":4.4363,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.95164925,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"335","last_page":"353"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9987000226974487,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9984999895095825,"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/axiom","display_name":"Axiom","score":0.7928000092506409},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.7002999782562256},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.5418999791145325},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.5127000212669373},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.4625999927520752},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.4350999891757965},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.4207000136375427},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.40130001306533813},{"id":"https://openalex.org/keywords/modalities","display_name":"Modalities","score":0.39430001378059387},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3776000142097473}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7928000092506409},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.7002999782562256},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6859999895095825},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.5418999791145325},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.5127000212669373},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.4625999927520752},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4366999864578247},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.4350999891757965},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.4207000136375427},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.40130001306533813},{"id":"https://openalex.org/C2779903281","wikidata":"https://www.wikidata.org/wiki/Q6888026","display_name":"Modalities","level":2,"score":0.39430001378059387},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38749998807907104},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3776000142097473},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.35760000348091125},{"id":"https://openalex.org/C125773388","wikidata":"https://www.wikidata.org/wiki/Q792542","display_name":"Axiomatic system","level":3,"score":0.352400004863739},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.32249999046325684},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.32199999690055847},{"id":"https://openalex.org/C134752490","wikidata":"https://www.wikidata.org/wiki/Q374182","display_name":"Logical consequence","level":2,"score":0.31520000100135803},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2992999851703644},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.29409998655319214},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29330000281333923},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.29319998621940613},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.2833999991416931},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.2833000123500824},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.2750999927520752},{"id":"https://openalex.org/C13766981","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Automated proof checking","level":3,"score":0.27379998564720154},{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C56949724","wikidata":"https://www.wikidata.org/wiki/Q219079","display_name":"Truth table","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C2780226545","wikidata":"https://www.wikidata.org/wiki/Q6888030","display_name":"Modality (human\u2013computer interaction)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.2572000026702881}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-032-06085-3_18","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-06085-3_18","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-06085-3_18.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"}],"best_oa_location":{"id":"doi:10.1007/978-3-032-06085-3_18","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-06085-3_18","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-06085-3_18.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":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414570856.pdf"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W25419626","https://openalex.org/W26908971","https://openalex.org/W127701250","https://openalex.org/W1482262189","https://openalex.org/W1528233644","https://openalex.org/W1546574044","https://openalex.org/W1604435911","https://openalex.org/W1699512023","https://openalex.org/W1706340846","https://openalex.org/W1797159706","https://openalex.org/W1950219843","https://openalex.org/W2039977878","https://openalex.org/W2048526770","https://openalex.org/W2114469058","https://openalex.org/W2765937481","https://openalex.org/W2796622197","https://openalex.org/W3105116513","https://openalex.org/W4249736722","https://openalex.org/W4384344717"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,60,88],"consider":[2],"intuitionistic":[3],"multimodal":[4,69],"logics":[5],"with":[6],"modalities":[7,33],"satisfying":[8],"axiom":[9,13],"K":[10],"and":[11,25,34,47,54,98,140,147],"the":[12,80,91,123],"of":[14,20,36,45,52,57,138],"Necessity,":[15],"as":[16,18],"well":[17],"collections":[19],"axioms":[21,39],"for":[22,43,103,131],"transforming,":[23],"removing":[24],"splitting":[26],"modalities,":[27],"specified":[28],"by":[29,118],"a":[30,72,85,96,111,136],"relation":[31],"between":[32],"sequences":[35],"modalities.":[37],"These":[38],"can":[40,107,144],"be":[41,108,145],"used":[42],"systems":[44],"knowledge":[46],"belief,":[48],"describing":[49],"multiple":[50,133],"environments":[51],"truth":[53],"their":[55,141],"awareness":[56],"each":[58],"other.":[59],"extend":[61,79],"Gentzen\u2019s":[62],"decidable":[63],"cut-free":[64],"calculus":[65],"to":[66,78,94,149],"accommodate":[67],"such":[68],"systems,":[70],"using":[71,122],"modal":[73],"shift":[74],"operation":[75],"on":[76],"contexts":[77],"cut":[81,124],"elimination":[82],"proof":[83,101,128],"in":[84,110],"novel":[86],"way.":[87],"then":[89],"adapt":[90],"inverse":[92],"method":[93],"formulate":[95],"correct":[97],"complete":[99],"forward":[100],"search":[102,129],"these":[104],"logics,":[105],"which":[106,143],"interpreted":[109],"Fitch-style":[112],"manner.":[113],"Proof":[114],"derivation":[115],"is":[116],"streamlined":[117],"implementing":[119],"most":[120],"derivations":[121],"rule.":[125],"The":[126],"resulting":[127],"allows":[130],"making":[132],"queries,":[134],"building":[135],"database":[137],"assumptions":[139],"consequences":[142],"fine-tuned":[146],"updated":[148],"fit":[150],"an":[151],"application.":[152]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-04-06T07:47:59.780226","created_date":"2025-10-10T00:00:00"}