{"id":"https://openalex.org/W2790333035","doi":"https://doi.org/10.1093/logcom/exx044","title":"A proof-theoretic study of bi-intuitionistic propositional sequent calculus","display_name":"A proof-theoretic study of bi-intuitionistic propositional sequent calculus","publication_year":2017,"publication_date":"2017-12-01","ids":{"openalex":"https://openalex.org/W2790333035","doi":"https://doi.org/10.1093/logcom/exx044","mag":"2790333035"},"language":"en","primary_location":{"id":"doi:10.1093/logcom/exx044","is_oa":false,"landing_page_url":"https://doi.org/10.1093/logcom/exx044","pdf_url":null,"source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://hdl.handle.net/1822/58110","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063925293","display_name":"Lu\u00eds Pinto","orcid":"https://orcid.org/0000-0003-1338-2688"},"institutions":[{"id":"https://openalex.org/I99682543","display_name":"University of Minho","ror":"https://ror.org/037wpkx04","country_code":"PT","type":"education","lineage":["https://openalex.org/I99682543"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Lu\u00eds Pinto","raw_affiliation_strings":["Centro de Matem\u00e1tica, Universidade do Minho, Campus de Gualtar, Braga, Portugal"],"affiliations":[{"raw_affiliation_string":"Centro de Matem\u00e1tica, Universidade do Minho, Campus de Gualtar, Braga, Portugal","institution_ids":["https://openalex.org/I99682543"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074922343","display_name":"Tarmo Uustalu","orcid":"https://orcid.org/0000-0002-1297-0579"},"institutions":[{"id":"https://openalex.org/I111112146","display_name":"Tallinn University of Technology","ror":"https://ror.org/0443cwa12","country_code":"EE","type":"education","lineage":["https://openalex.org/I111112146"]}],"countries":["EE"],"is_corresponding":true,"raw_author_name":"Tarmo Uustalu","raw_affiliation_strings":["Institute of Cybernetics at Tallinn University of Technology, Tallinn, Estonia"],"affiliations":[{"raw_affiliation_string":"Institute of Cybernetics at Tallinn University of Technology, Tallinn, Estonia","institution_ids":["https://openalex.org/I111112146"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074922343"],"corresponding_institution_ids":["https://openalex.org/I111112146"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":{"value":4151,"currency":"USD","value_usd":4151},"fwci":0.2079,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.67558296,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"28","issue":"1","first_page":"165","last_page":"202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9993000030517578,"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":0.9965000152587891,"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":0.8369919657707214},{"id":"https://openalex.org/keywords/sequent-calculus","display_name":"Sequent calculus","score":0.8314465284347534},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.7376903295516968},{"id":"https://openalex.org/keywords/cut-elimination-theorem","display_name":"Cut-elimination theorem","score":0.6771117448806763},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.6464292407035828},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.6146782040596008},{"id":"https://openalex.org/keywords/proof-calculus","display_name":"Proof calculus","score":0.6112394332885742},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.6049152612686157},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5736543536186218},{"id":"https://openalex.org/keywords/structural-proof-theory","display_name":"Structural proof theory","score":0.503053605556488},{"id":"https://openalex.org/keywords/curry\u2013howard-correspondence","display_name":"Curry\u2013Howard correspondence","score":0.5000615119934082},{"id":"https://openalex.org/keywords/kripke-semantics","display_name":"Kripke semantics","score":0.4876638650894165},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.4120435118675232},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.378385066986084},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3528951406478882},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2827846109867096},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.23946481943130493},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.22504934668540955},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20756712555885315},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10428515076637268},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.08596983551979065}],"concepts":[{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.8369919657707214},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.8314465284347534},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.7376903295516968},{"id":"https://openalex.org/C111404639","wikidata":"https://www.wikidata.org/wiki/Q376166","display_name":"Cut-elimination theorem","level":4,"score":0.6771117448806763},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.6464292407035828},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.6146782040596008},{"id":"https://openalex.org/C6489637","wikidata":"https://www.wikidata.org/wiki/Q7250002","display_name":"Proof calculus","level":3,"score":0.6112394332885742},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.6049152612686157},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5736543536186218},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.503053605556488},{"id":"https://openalex.org/C85343465","wikidata":"https://www.wikidata.org/wiki/Q975734","display_name":"Curry\u2013Howard correspondence","level":3,"score":0.5000615119934082},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.4876638650894165},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.4120435118675232},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.378385066986084},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3528951406478882},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2827846109867096},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.23946481943130493},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.22504934668540955},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20756712555885315},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10428515076637268},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.08596983551979065},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1093/logcom/exx044","is_oa":false,"landing_page_url":"https://doi.org/10.1093/logcom/exx044","pdf_url":null,"source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},{"id":"pmh:oai:repositorium.uminho.pt:1822/58110","is_oa":true,"landing_page_url":"https://hdl.handle.net/1822/58110","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repositorium.sdum.uminho.pt:1822/58110","is_oa":true,"landing_page_url":"http://hdl.handle.net/1822/58110","pdf_url":null,"source":{"id":"https://openalex.org/S4306400354","display_name":"Reposit\u00f3riUM (Universidade do Minho)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99682543","host_organization_name":"University of Minho","host_organization_lineage":["https://openalex.org/I99682543"],"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":"","raw_type":null}],"best_oa_location":{"id":"pmh:oai:repositorium.uminho.pt:1822/58110","is_oa":true,"landing_page_url":"https://hdl.handle.net/1822/58110","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"score":0.8100000023841858,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G4308801520","display_name":null,"funder_award_id":"6940","funder_id":"https://openalex.org/F4320321018","funder_display_name":"Eesti Teadusfondi"}],"funders":[{"id":"https://openalex.org/F4320321018","display_name":"Eesti Teadusfondi","ror":"https://ror.org/00jjeja18"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W173108123","https://openalex.org/W1483568252","https://openalex.org/W1503796635","https://openalex.org/W1568501149","https://openalex.org/W1602312920","https://openalex.org/W1836554196","https://openalex.org/W1854821975","https://openalex.org/W1968581827","https://openalex.org/W1990123412","https://openalex.org/W1992582651","https://openalex.org/W1993745552","https://openalex.org/W1995718667","https://openalex.org/W2014085418","https://openalex.org/W2016326123","https://openalex.org/W2027162606","https://openalex.org/W2044300637","https://openalex.org/W2051358061","https://openalex.org/W2077879002","https://openalex.org/W2093705378","https://openalex.org/W2131739376","https://openalex.org/W2134382089","https://openalex.org/W2135986646","https://openalex.org/W2146345041","https://openalex.org/W2147768374","https://openalex.org/W2160399032","https://openalex.org/W2185755248","https://openalex.org/W2231337787","https://openalex.org/W2476903666","https://openalex.org/W2508249339","https://openalex.org/W2559873117","https://openalex.org/W2912464567","https://openalex.org/W3037496313","https://openalex.org/W3048760744","https://openalex.org/W3127557058","https://openalex.org/W3135320517","https://openalex.org/W3150713206","https://openalex.org/W4210927669","https://openalex.org/W6638926533","https://openalex.org/W6639202083","https://openalex.org/W6642364823","https://openalex.org/W6680275991","https://openalex.org/W6793870685"],"related_works":["https://openalex.org/W2134382089","https://openalex.org/W162254089","https://openalex.org/W2033813295","https://openalex.org/W1484266479","https://openalex.org/W1492421865","https://openalex.org/W4289719525","https://openalex.org/W1557149243","https://openalex.org/W2170954486","https://openalex.org/W2108922266","https://openalex.org/W1510709103"],"abstract_inverted_index":{"Bi-intuitionistic":[0],"logic":[1,8,24,35,84],"is":[2,25,68],"the":[3,41,46,50,71,76,129,133,172,176,184,190,197,201,206,214,217,221,229,235,282,288],"conservative":[4],"extension":[5],"of":[6,78,99,113,125,136,156,175,196,284,290],"intuitionistic":[7,34],"with":[9,36,89,264],"a":[10,97,123,153,244,250,261,278],"connective":[11],"dual":[12,39],"to":[13,40,52,57,142,186,224,274],"implication":[14,42],"usually":[15],"called":[16],"\u2018exclusion\u2019.":[17],"A":[18],"standard-style":[19,58,202],"sequent":[20,31,59,159],"calculus":[21,32,67,98,124,178,199,203,246,263],"for":[22,33,61,81,109,161,189],"this":[23,66,149],"easily":[26],"obtained":[27],"by":[28,75,102,128,170],"extending":[29],"multiple-conclusion":[30],"exclusion":[37],"rules":[38,43,108,208],"(in":[44,277],"particular,":[45],"exclusion-left":[47],"rule":[48],"restricts":[49],"premise":[51],"be":[53,225,275],"single-assumption).":[54],"However,":[55],"similarly":[56],"calculi":[60,88,160,219,273],"non-classical":[62],"logics":[63],"like":[64],"S5,":[65],"incomplete":[69],"without":[70],"cut":[72],"rule.":[73],"Motivated":[74],"problem":[77],"proof":[79],"search":[80],"propositional":[82],"bi-intuitionistic":[83],"(BiInt),":[85],"various":[86],"cut-free":[87],"extended":[90],"sequents":[91,101,127,248,285],"have":[92,249],"been":[93],"proposed,":[94],"including":[95],"(i)":[96,243],"nested":[100,198,218,262],"Gor\u00e9":[103],"et":[104],"al.,":[105],"which":[106,138,255],"includes":[107,139,256],"creation":[110],"and":[111,121,181,216,234,254,259,266,269,286],"removal":[112],"nests":[114],"(called":[115],"\u2018nest":[116],"rules\u2019,":[117],"resp.":[118],"\u2018unnest":[119],"rules\u2019)":[120],"(ii)":[122,260],"labelled":[126,177,215,245],"authors,":[130],"derived":[131],"from":[132],"Kripke":[134],"semantics":[135],"BiInt,":[137],"\u2018monotonicity":[140],"rules\u2019":[141,258],"propagate":[143],"truth/falsehood":[144],"between":[145,166,213],"accessible":[146],"worlds.":[147],"In":[148],"paper,":[150],"we":[151,240],"develop":[152],"proof-theoretic":[154],"study":[155],"these":[157,271],"three":[158],"BiInt":[162],"grounded":[163],"on":[164],"translations":[165,185,212],"them.":[167],"We":[168],"start":[169],"establishing":[171],"basic":[173],"meta-theory":[174],"(including":[179],"cut-admissibility),":[180],"use":[182],"then":[183],"obtain":[187],"results":[188],"other":[191],"two":[192,222,272],"calculi.":[193],"The":[194,211],"translation":[195],"into":[200],"explains":[204],"how":[205],"unnest":[207],"encapsulate":[209],"cuts.":[210],"reveal":[220],"formats":[223],"very":[226],"close,":[227],"despite":[228],"former":[230],"incorporating":[231],"semantic":[232],"elements,":[233],"latter":[236],"being":[237],"syntax-driven.":[238],"Indeed,":[239],"single":[241],"out":[242],"whose":[247],"\u2018label":[251],"in":[252],"focus\u2019":[253],"\u2018refocusing":[257],"monotonicity":[265],"refocusing":[267],"rules,":[268],"prove":[270],"isomorphic":[276],"bijection":[279],"both":[280],"at":[281,287],"level":[283,289],"derivations).":[291]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}