{"id":"https://openalex.org/W2183553861","doi":"https://doi.org/10.3233/fi-2015-1253","title":"A Semantical Analysis of Focusing and Contraction in Intuitionistic Logic","display_name":"A Semantical Analysis of Focusing and Contraction in Intuitionistic Logic","publication_year":2015,"publication_date":"2015-09-14","ids":{"openalex":"https://openalex.org/W2183553861","doi":"https://doi.org/10.3233/fi-2015-1253","mag":"2183553861"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2015-1253","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2015-1253","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-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/A5048799091","display_name":"Alessandro Avellone","orcid":"https://orcid.org/0000-0003-1677-1005"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Alessandro Avellone","raw_affiliation_strings":["Dipartimenti di Statistica e Metodi Quantitativi, Universit\u00e0 degli Studi di Milano-Bicocca, Italy. alessandro.avellone@unimib.it"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimenti di Statistica e Metodi Quantitativi, Universit\u00e0 degli Studi di Milano-Bicocca, Italy. alessandro.avellone@unimib.it","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011583391","display_name":"Camillo Fiorentini","orcid":"https://orcid.org/0000-0003-2152-7488"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Camillo Fiorentini","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 degli Studi di Milano, Italy. fiorentini@di.unimi.it; momigliano@di.unimi.it"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 degli Studi di Milano, Italy. fiorentini@di.unimi.it; momigliano@di.unimi.it","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021883093","display_name":"Alberto Momigliano","orcid":"https://orcid.org/0000-0003-0942-4777"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alberto Momigliano","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 degli Studi di Milano, Italy. fiorentini@di.unimi.it; momigliano@di.unimi.it"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 degli Studi di Milano, Italy. fiorentini@di.unimi.it; momigliano@di.unimi.it","institution_ids":["https://openalex.org/I189158943"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048799091"],"corresponding_institution_ids":["https://openalex.org/I66752286"],"apc_list":null,"apc_paid":null,"fwci":0.5264,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.81817156,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"140","issue":"3-4","first_page":"247","last_page":"262"},"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":0.9993000030517578,"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":0.9922000169754028,"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/cut-elimination-theorem","display_name":"Cut-elimination theorem","score":0.7809745669364929},{"id":"https://openalex.org/keywords/proof-calculus","display_name":"Proof calculus","score":0.7720797061920166},{"id":"https://openalex.org/keywords/sequent","display_name":"Sequent","score":0.7689090967178345},{"id":"https://openalex.org/keywords/sequent-calculus","display_name":"Sequent calculus","score":0.7409278154373169},{"id":"https://openalex.org/keywords/structural-proof-theory","display_name":"Structural proof theory","score":0.7374852895736694},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.695342481136322},{"id":"https://openalex.org/keywords/curry\u2013howard-correspondence","display_name":"Curry\u2013Howard correspondence","score":0.6056776642799377},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.5869226455688477},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5532233715057373},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5448328256607056},{"id":"https://openalex.org/keywords/rule-of-inference","display_name":"Rule of inference","score":0.5107090473175049},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.5004355907440186},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.4880918264389038},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.4691544771194458},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4539808928966522},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.44484877586364746},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.4336680471897125},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.4324703812599182},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4125377833843231},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3124036192893982},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11551705002784729}],"concepts":[{"id":"https://openalex.org/C111404639","wikidata":"https://www.wikidata.org/wiki/Q376166","display_name":"Cut-elimination theorem","level":4,"score":0.7809745669364929},{"id":"https://openalex.org/C6489637","wikidata":"https://www.wikidata.org/wiki/Q7250002","display_name":"Proof calculus","level":3,"score":0.7720797061920166},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.7689090967178345},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.7409278154373169},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.7374852895736694},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.695342481136322},{"id":"https://openalex.org/C85343465","wikidata":"https://www.wikidata.org/wiki/Q975734","display_name":"Curry\u2013Howard correspondence","level":3,"score":0.6056776642799377},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.5869226455688477},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5532233715057373},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5448328256607056},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.5107090473175049},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.5004355907440186},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.4880918264389038},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.4691544771194458},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4539808928966522},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.44484877586364746},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.4336680471897125},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.4324703812599182},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4125377833843231},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3124036192893982},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11551705002784729},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3233/fi-2015-1253","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2015-1253","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},{"id":"pmh:oai:boa.unimib.it:10281/88857","is_oa":false,"landing_page_url":"http://hdl.handle.net/10281/88857","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W60804773","https://openalex.org/W119332729","https://openalex.org/W127064451","https://openalex.org/W203185353","https://openalex.org/W265101905","https://openalex.org/W1487717359","https://openalex.org/W1503796635","https://openalex.org/W1507932752","https://openalex.org/W1571434350","https://openalex.org/W1579056021","https://openalex.org/W1795577507","https://openalex.org/W1807903125","https://openalex.org/W1852594029","https://openalex.org/W1971769584","https://openalex.org/W1989085426","https://openalex.org/W2008788038","https://openalex.org/W2009938424","https://openalex.org/W2030232034","https://openalex.org/W2033813295","https://openalex.org/W2070324762","https://openalex.org/W2087005564","https://openalex.org/W2088881461","https://openalex.org/W2093111544","https://openalex.org/W2113939721","https://openalex.org/W2124047678","https://openalex.org/W2131739376","https://openalex.org/W2134005639","https://openalex.org/W2141039045","https://openalex.org/W2141978322","https://openalex.org/W2188691967","https://openalex.org/W2242812693","https://openalex.org/W2572761669"],"related_works":["https://openalex.org/W2134382089","https://openalex.org/W162254089","https://openalex.org/W1534718845","https://openalex.org/W1492421865","https://openalex.org/W2033813295","https://openalex.org/W1484266479","https://openalex.org/W2591349272","https://openalex.org/W2913240377","https://openalex.org/W2753667555","https://openalex.org/W1807903125"],"abstract_inverted_index":{"Focusing":[0],"is":[1,31],"a":[2,15,61,99],"proof-theoretic":[3],"device":[4],"to":[5,18,102],"structure":[6],"proof":[7],"search":[8],"in":[9,21,33,51,55,79],"the":[10,23,76,80,91],"sequent":[11,68],"calculus:":[12],"it":[13],"provides":[14],"normal":[16],"form":[17],"cut-free":[19],"proofs":[20],"which":[22,74],"application":[24],"of":[25,82,90],"invertible":[26],"and":[27,36,85,94],"non-invertible":[28],"inference":[29],"rules":[30],"structured":[32],"two":[34],"separate":[35],"disjoint":[37],"phases.":[38],"Although":[39],"stemming":[40],"from":[41],"proof-search":[42],"cons":[43],"iderations,":[44],"focusing":[45],"has":[46],"not":[47],"been":[48],"thoroughly":[49],"investigated":[50],"actual":[52],"theorem":[53],"proving,":[54],"particular":[56],"w.r.t.":[57],"termination.":[58],"We":[59,87],"present":[60],"contraction-free":[62],"(and":[63],"hence":[64],"terminating)":[65],"focused":[66],"multi-succedent":[67],"calculus":[69,78,92],"for":[70],"propositional":[71],"intuitionistic":[72],"logic,":[73],"refines":[75],"G4ip":[77],"tradition":[81],"Vorob\u2019ev,":[83],"Hudelmeier":[84],"Dyckhoff.":[86],"prove":[88],"completeness":[89],"semantically":[93],"argue":[95],"that":[96],"this":[97],"offers":[98],"viable":[100],"alternative":[101],"other":[103],"more":[104],"syntactical":[105],"means.":[106]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}