{"id":"https://openalex.org/W4237528529","doi":"https://doi.org/10.1109/lics.2004.1319615","title":"On the geometry of interaction for classical logic","display_name":"On the geometry of interaction for classical logic","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W4237528529","doi":"https://doi.org/10.1109/lics.2004.1319615"},"language":"en","primary_location":{"id":"doi:10.1109/lics.2004.1319615","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics.2004.1319615","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082534690","display_name":"Carsten F\u00fchrmann","orcid":null},"institutions":[{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"C. Fuhrmann","raw_affiliation_strings":["University of Bath, UK"],"affiliations":[{"raw_affiliation_string":"University of Bath, UK","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013218535","display_name":"David Pym","orcid":"https://orcid.org/0000-0002-6504-5838"},"institutions":[{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"D. Pym","raw_affiliation_strings":["University of Bath, UK"],"affiliations":[{"raw_affiliation_string":"University of Bath, UK","institution_ids":["https://openalex.org/I51601045"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082534690"],"corresponding_institution_ids":["https://openalex.org/I51601045"],"apc_list":null,"apc_paid":null,"fwci":4.4971,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.94818836,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"417","issue":null,"first_page":"211","last_page":"220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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/T10126","display_name":"Logic, programming, and type systems","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/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/T10142","display_name":"Formal Methods in Verification","score":0.9958999752998352,"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/morphism","display_name":"Morphism","score":0.6476966142654419},{"id":"https://openalex.org/keywords/sequent-calculus","display_name":"Sequent calculus","score":0.6222354173660278},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.5138511657714844},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47866448760032654},{"id":"https://openalex.org/keywords/sequent","display_name":"Sequent","score":0.46510109305381775},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43084388971328735},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.42527931928634644},{"id":"https://openalex.org/keywords/classical-logic","display_name":"Classical logic","score":0.424567848443985},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"First-order logic","score":0.41884803771972656},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37309008836746216},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3578210473060608},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3494570851325989},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2787652015686035},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26305070519447327},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2524956464767456}],"concepts":[{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.6476966142654419},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.6222354173660278},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.5138511657714844},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47866448760032654},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.46510109305381775},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43084388971328735},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.42527931928634644},{"id":"https://openalex.org/C32241873","wikidata":"https://www.wikidata.org/wiki/Q236975","display_name":"Classical logic","level":2,"score":0.424567848443985},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.41884803771972656},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37309008836746216},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3578210473060608},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3494570851325989},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2787652015686035},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26305070519447327},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2524956464767456},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"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/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lics.2004.1319615","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics.2004.1319615","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6100000143051147,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1485153875","https://openalex.org/W1488538795","https://openalex.org/W1968350036","https://openalex.org/W1993205599","https://openalex.org/W2008920425","https://openalex.org/W2015626965","https://openalex.org/W2018773995","https://openalex.org/W2039977878","https://openalex.org/W2051450758","https://openalex.org/W2078051080","https://openalex.org/W2096885339","https://openalex.org/W2102357532","https://openalex.org/W2120713972","https://openalex.org/W2152013675","https://openalex.org/W2911865844","https://openalex.org/W4237528529","https://openalex.org/W6674435064"],"related_works":["https://openalex.org/W4253113110","https://openalex.org/W2096191306","https://openalex.org/W2137780954","https://openalex.org/W1771892589","https://openalex.org/W4293309763","https://openalex.org/W2096038201","https://openalex.org/W2008876986","https://openalex.org/W1499822848","https://openalex.org/W2949724905","https://openalex.org/W2033347591"],"abstract_inverted_index":{"It":[0],"is":[1],"well-known":[2],"that":[3,27],"weakening":[4,69],"and":[5,24,57,70,86],"contraction":[6],"cause":[7],"naive":[8],"categorical":[9],"models":[10,26,46,61,73],"of":[11,44,68,80,90],"the":[12,49,66],"classical":[13,81],"sequent":[14],"calculus":[15],"to":[16,18,52,77],"collapse":[17,30],"Boolean":[19],"lattices.":[20],"We":[21,40],"introduce":[22],"sound":[23],"complete":[25],"avoid":[28],"this":[29],"by":[31,34,47],"interpreting":[32],"cut-reduction":[33],"a":[35],"partial":[36],"order":[37],"between":[38],"morphisms.":[39],"provide":[41],"concrete":[42],"examples":[43],"such":[45],"applying":[48],"geometry-of-interaction":[50],"construction":[51],"quantaloids":[53],"with":[54],"finite":[55],"biproducts,":[56],"show":[58],"how":[59],"these":[60],"illuminate":[62],"cut":[63],"reduction":[64],"in":[65],"presence":[67],"contraction.":[71],"Our":[72],"make":[74],"no":[75],"commitment":[76],"any":[78],"translation":[79],"logic":[82,85],"into":[83],"intuitionistic":[84],"distinguish":[87],"non-deterministic":[88],"choices":[89],"cut-elimination.":[91]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}