{"id":"https://openalex.org/W4386363699","doi":"https://doi.org/10.1007/978-3-031-38499-8_19","title":"A Uniform Formalisation of\u00a0Three-Valued Logics in\u00a0Bisequent Calculus","display_name":"A Uniform Formalisation of\u00a0Three-Valued Logics in\u00a0Bisequent Calculus","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4386363699","doi":"https://doi.org/10.1007/978-3-031-38499-8_19"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-38499-8_19","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-38499-8_19","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-38499-8_19.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/10.1007/978-3-031-38499-8_19.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036443124","display_name":"Andrzej Indrzejczak","orcid":"https://orcid.org/0000-0003-4063-1651"},"institutions":[{"id":"https://openalex.org/I34250744","display_name":"University of \u0141\u00f3d\u017a","ror":"https://ror.org/05cq64r17","country_code":"PL","type":"education","lineage":["https://openalex.org/I34250744"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Andrzej Indrzejczak","raw_affiliation_strings":["Department of Logic, University of Lodz, \u0141\u00f3d\u017a, Poland"],"raw_orcid":"https://orcid.org/0000-0003-4063-1651","affiliations":[{"raw_affiliation_string":"Department of Logic, University of Lodz, \u0141\u00f3d\u017a, Poland","institution_ids":["https://openalex.org/I34250744"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032808113","display_name":"Yaroslav Petrukhin","orcid":"https://orcid.org/0000-0002-7731-1339"},"institutions":[{"id":"https://openalex.org/I34250744","display_name":"University of \u0141\u00f3d\u017a","ror":"https://ror.org/05cq64r17","country_code":"PL","type":"education","lineage":["https://openalex.org/I34250744"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Yaroslav Petrukhin","raw_affiliation_strings":["Department of Logic, University of Lodz, \u0141\u00f3d\u017a, Poland"],"raw_orcid":"https://orcid.org/0000-0002-7731-1339","affiliations":[{"raw_affiliation_string":"Department of Logic, University of Lodz, \u0141\u00f3d\u017a, Poland","institution_ids":["https://openalex.org/I34250744"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036443124"],"corresponding_institution_ids":["https://openalex.org/I34250744"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":2.0217,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.88185335,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"325","last_page":"343"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","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"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","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":0.9991999864578247,"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":0.9983000159263611,"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/sequent","display_name":"Sequent","score":0.7226898670196533},{"id":"https://openalex.org/keywords/sequent-calculus","display_name":"Sequent calculus","score":0.6351245641708374},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.5700543522834778},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5333521366119385},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47817832231521606},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4744737446308136},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4352520704269409},{"id":"https://openalex.org/keywords/cut-elimination-theorem","display_name":"Cut-elimination theorem","score":0.42527398467063904},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42489922046661377},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4228990972042084},{"id":"https://openalex.org/keywords/proof-calculus","display_name":"Proof calculus","score":0.35144150257110596},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3444897532463074},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.32155442237854004},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3154228925704956},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.06142410635948181},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05985113978385925},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.053429245948791504}],"concepts":[{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.7226898670196533},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.6351245641708374},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.5700543522834778},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5333521366119385},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47817832231521606},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4744737446308136},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4352520704269409},{"id":"https://openalex.org/C111404639","wikidata":"https://www.wikidata.org/wiki/Q376166","display_name":"Cut-elimination theorem","level":4,"score":0.42527398467063904},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42489922046661377},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4228990972042084},{"id":"https://openalex.org/C6489637","wikidata":"https://www.wikidata.org/wiki/Q7250002","display_name":"Proof calculus","level":3,"score":0.35144150257110596},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3444897532463074},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.32155442237854004},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3154228925704956},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.06142410635948181},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05985113978385925},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.053429245948791504},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-38499-8_19","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-38499-8_19","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-38499-8_19.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:10.1007/978-3-031-38499-8_19","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-38499-8_19","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-38499-8_19.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":[{"id":"https://openalex.org/G5388102594","display_name":"Coming to Terms: Proof Theory Extended to Definite Descriptions and other Terms","funder_award_id":"101054714","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4386363699.pdf"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W607239742","https://openalex.org/W1511652686","https://openalex.org/W1986497773","https://openalex.org/W1990115729","https://openalex.org/W1994527472","https://openalex.org/W1994590553","https://openalex.org/W1996579835","https://openalex.org/W2002522556","https://openalex.org/W2006426192","https://openalex.org/W2036869460","https://openalex.org/W2037995299","https://openalex.org/W2048502195","https://openalex.org/W2058748845","https://openalex.org/W2062996390","https://openalex.org/W2067005442","https://openalex.org/W2085956853","https://openalex.org/W2092490196","https://openalex.org/W2104730696","https://openalex.org/W2142616542","https://openalex.org/W2166089338","https://openalex.org/W2319549361","https://openalex.org/W2607009070","https://openalex.org/W2800354409","https://openalex.org/W2952657320","https://openalex.org/W2969501000","https://openalex.org/W2981680275","https://openalex.org/W3110798604","https://openalex.org/W3194705343","https://openalex.org/W3198316942","https://openalex.org/W3202656763","https://openalex.org/W4249259371","https://openalex.org/W4253656749","https://openalex.org/W4388218653"],"related_works":["https://openalex.org/W4295728898","https://openalex.org/W3090765541","https://openalex.org/W2584381231","https://openalex.org/W1562648369","https://openalex.org/W4236940717","https://openalex.org/W2137780954","https://openalex.org/W2056025285","https://openalex.org/W2023557900","https://openalex.org/W162254089","https://openalex.org/W4253113110"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"present":[2],"a":[3,17,108],"uniform":[4],"characterisation":[5],"of":[6,11,20,31,42,48,57,65,98,110,123],"three-valued":[7,111],"logics":[8,112],"by":[9],"means":[10],"bisequent":[12,124],"calculus":[13,22],"(BSC).":[14],"It":[15,80],"is":[16,101,140],"generalised":[18,49],"form":[19],"sequent":[21,69],"(SC)":[23],"where":[24],"rules":[25],"operate":[26],"on":[27,52],"the":[28,39,45,121,133,137],"ordered":[29],"pairs":[30],"ordinary":[32,58],"sequents.":[33,59],"BSC":[34],"may":[35],"be":[36,118],"treated":[37],"as":[38],"weakest":[40],"kind":[41],"system":[43],"in":[44,120],"rich":[46],"family":[47,61],"SC":[50,75,100],"operating":[51],"items":[53],"being":[54],"some":[55,88,144],"collections":[56],"This":[60],"covers":[62],"several":[63,77],"forms":[64],"hypersequent":[66],"and":[67,91,113,131],"nested":[68],"calculi":[70],"introduced":[71],"to":[72],"provide":[73],"decent":[74],"for":[76,83,143],"non-classical":[78,85],"logics.":[79,145],"seems":[81],"that":[82],"many":[84],"logics,":[86,93],"including":[87],"many-valued,":[89],"paraconsistent":[90],"modal":[92],"this":[94,104],"reasonably":[95],"modest":[96],"generalization":[97],"standard":[99],"sufficient.":[102],"In":[103],"paper":[105],"we":[106],"examine":[107],"variety":[109],"show":[114],"how":[115],"they":[116],"can":[117],"formalised":[119],"framework":[122],"calculus.":[125],"All":[126],"provided":[127],"systems":[128],"are":[129],"cut-free":[130],"satisfy":[132],"subformula":[134],"property.":[135],"Also":[136],"interpolation":[138],"theorem":[139],"constructively":[141],"proved":[142]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
