{"id":"https://openalex.org/W1975460819","doi":"https://doi.org/10.2168/lmcs-2(2:4)2006","title":"A System of Interaction and Structure II: The Need for Deep Inference","display_name":"A System of Interaction and Structure II: The Need for Deep Inference","publication_year":2006,"publication_date":"2006-04-03","ids":{"openalex":"https://openalex.org/W1975460819","doi":"https://doi.org/10.2168/lmcs-2(2:4)2006","mag":"1975460819"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-2(2:4)2006","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-2(2:4)2006","pdf_url":"https://lmcs.episciences.org/2252/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/2252/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071064651","display_name":"Alwen Tiu","orcid":"https://orcid.org/0000-0002-2695-5636"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Alwen Tiu","raw_affiliation_strings":["Computer Science Laboratory, Research School in Information Science and Engineering, Australian National University, Canberra ACT 0200, Australia","Australian National University"],"affiliations":[{"raw_affiliation_string":"Computer Science Laboratory, Research School in Information Science and Engineering, Australian National University, Canberra ACT 0200, Australia","institution_ids":[]},{"raw_affiliation_string":"Australian National University","institution_ids":["https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071064651"],"corresponding_institution_ids":["https://openalex.org/I118347636"],"apc_list":null,"apc_paid":null,"fwci":8.3737,"has_fulltext":true,"cited_by_count":52,"citation_normalized_percentile":{"value":0.97332332,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"Volume 2, Issue 2","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","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/T10142","display_name":"Formal Methods in Verification","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sequent-calculus","display_name":"Sequent calculus","score":0.850052535533905},{"id":"https://openalex.org/keywords/proof-calculus","display_name":"Proof calculus","score":0.8310731649398804},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.789340615272522},{"id":"https://openalex.org/keywords/rule-of-inference","display_name":"Rule of inference","score":0.746974766254425},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.7022782564163208},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.6617911458015442},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.646134078502655},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.5345157384872437},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5150191783905029},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.48664388060569763},{"id":"https://openalex.org/keywords/sequent","display_name":"Sequent","score":0.4544821083545685},{"id":"https://openalex.org/keywords/logical-connective","display_name":"Logical connective","score":0.43252331018447876},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.41432690620422363},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4136275053024292},{"id":"https://openalex.org/keywords/conservative-extension","display_name":"Conservative extension","score":0.41102084517478943},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4105762541294098},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40486541390419006},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4027841091156006},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4025343060493469},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32013511657714844},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28859299421310425},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19951003789901733},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.14756715297698975}],"concepts":[{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.850052535533905},{"id":"https://openalex.org/C6489637","wikidata":"https://www.wikidata.org/wiki/Q7250002","display_name":"Proof calculus","level":3,"score":0.8310731649398804},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.789340615272522},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.746974766254425},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.7022782564163208},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.6617911458015442},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.646134078502655},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.5345157384872437},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5150191783905029},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.48664388060569763},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.4544821083545685},{"id":"https://openalex.org/C194989596","wikidata":"https://www.wikidata.org/wiki/Q211790","display_name":"Logical connective","level":2,"score":0.43252331018447876},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41432690620422363},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4136275053024292},{"id":"https://openalex.org/C2780432614","wikidata":"https://www.wikidata.org/wiki/Q864213","display_name":"Conservative extension","level":2,"score":0.41102084517478943},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4105762541294098},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40486541390419006},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4027841091156006},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4025343060493469},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32013511657714844},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28859299421310425},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19951003789901733},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.14756715297698975},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.2168/lmcs-2(2:4)2006","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-2(2:4)2006","pdf_url":"https://lmcs.episciences.org/2252/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:cs/0512036","is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/0512036","pdf_url":"https://arxiv.org/pdf/cs/0512036","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.342.6238","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.342.6238","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cs/0512036v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.59.4693","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.59.4693","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/~tiu/deep.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:edda78b01d3e480eb895d69c95e5785d","is_oa":true,"landing_page_url":"https://doaj.org/article/edda78b01d3e480eb895d69c95e5785d","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 2, Issue 2 (2006)","raw_type":"article"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:10440/505","is_oa":true,"landing_page_url":"http://hdl.handle.net/10440/505","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"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":"Logical Methods in Computer Science","raw_type":"Journal article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-2(2:4)2006","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-2(2:4)2006","pdf_url":"https://lmcs.episciences.org/2252/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320313934","display_name":"Institut national de recherche en informatique et en automatique (INRIA)","ror":"https://ror.org/02kvxyf05"},{"id":"https://openalex.org/F4320321613","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1975460819.pdf","grobid_xml":"https://content.openalex.org/works/W1975460819.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W64134619","https://openalex.org/W172885811","https://openalex.org/W1494188379","https://openalex.org/W1585310225","https://openalex.org/W1598954248","https://openalex.org/W1755291416","https://openalex.org/W1795577507","https://openalex.org/W1811725859","https://openalex.org/W2008132476","https://openalex.org/W2089177783","https://openalex.org/W2095436832","https://openalex.org/W2102625227","https://openalex.org/W2117737141","https://openalex.org/W2168747849","https://openalex.org/W2911865844","https://openalex.org/W3135320517","https://openalex.org/W3146910854","https://openalex.org/W4210927669","https://openalex.org/W4248156396","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W117036793","https://openalex.org/W2061801837","https://openalex.org/W2210298890","https://openalex.org/W2124344212","https://openalex.org/W2163170048","https://openalex.org/W2290333159","https://openalex.org/W2102625227","https://openalex.org/W2099353057","https://openalex.org/W1975460819","https://openalex.org/W2107905351"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"properties":[3],"of":[4,12,28,51,102,106],"the":[5,26,64,92,100,103],"logic":[6,15,93],"BV,":[7,94],"which":[8,39,68],"is":[9,23,86],"an":[10],"extension":[11],"multiplicative":[13],"linear":[14],"(MLL)":[16],"with":[17,63],"a":[18,30,56,111],"self-dual":[19,65],"non-commutative":[20,66],"operator.":[21],"BV":[22,107],"presented":[24],"in":[25,38,55,78,110],"calculus":[27],"structures,":[29],"proof":[31],"theoretic":[32],"formalism":[33],"that":[34,95],"supports":[35],"deep":[36,52,84],"inference,":[37],"inference":[40,53,85,104],"rules":[41,105],"can":[42],"be":[43,76,89],"applied":[44],"anywhere":[45],"inside":[46],"logical":[47,58,115],"expressions.":[48],"The":[49],"use":[50],"results":[54],"simple":[57],"system":[59],"for":[60,91],"MLL":[61],"extended":[62],"operator,":[67],"has":[69],"been":[70],"to":[71,75,88],"date":[72],"not":[73],"known":[74],"expressible":[77],"sequent":[79],"calculus.":[80],"In":[81],"this":[82],"paper,":[83],"shown":[87],"crucial":[90],"is,":[96],"any":[97],"restriction":[98],"on":[99],"``depth''":[101],"would":[108],"result":[109],"strictly":[112],"less":[113],"expressive":[114],"system.":[116]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}