{"id":"https://openalex.org/W2134446632","doi":"https://doi.org/10.2178/jsl/1129642117","title":"The geometry of non-distributive logics","display_name":"The geometry of non-distributive logics","publication_year":2005,"publication_date":"2005-12-01","ids":{"openalex":"https://openalex.org/W2134446632","doi":"https://doi.org/10.2178/jsl/1129642117","mag":"2134446632"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1129642117","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://consequently.org/papers/gndl.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009371587","display_name":"Greg Restall","orcid":"https://orcid.org/0000-0001-8257-6764"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Greg Restall","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101735626","display_name":"Francesco Paoli","orcid":"https://orcid.org/0000-0001-7915-3832"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Francesco Paoli","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":14,"citation_normalized_percentile":{"value":0.867364,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":84,"max":85},"biblio":{"volume":"70","issue":"4","first_page":"1108","last_page":"1126"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9997,"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":0.9997,"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":0.9984,"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":0.9877,"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","display_name":"Sequent","score":0.67459226},{"id":"https://openalex.org/keywords/classical-logic","display_name":"Classical logic","score":0.4722416},{"id":"https://openalex.org/keywords/negation","display_name":"Negation","score":0.46962905}],"concepts":[{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.77633774},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.77134216},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.67459226},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5932317},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.5184471},{"id":"https://openalex.org/C32241873","wikidata":"https://www.wikidata.org/wiki/Q236975","display_name":"Classical logic","level":2,"score":0.4722416},{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.46962905},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.41201323},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39885706},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.39547408},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3904545},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.37560517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.344904},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32287282},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2773516},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.21408573},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.20701835},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.121916175},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08070311},{"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}],"mesh":[],"locations_count":2,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1129642117","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.381.9101","pdf_url":"http://consequently.org/papers/gndl.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.381.9101","pdf_url":"http://consequently.org/papers/gndl.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":24,"referenced_works":["https://openalex.org/W1485574327","https://openalex.org/W1500907847","https://openalex.org/W1527995180","https://openalex.org/W1964454590","https://openalex.org/W1982425141","https://openalex.org/W1992153273","https://openalex.org/W2001483956","https://openalex.org/W2003017965","https://openalex.org/W2055247079","https://openalex.org/W2079171825","https://openalex.org/W2093397547","https://openalex.org/W2094993595","https://openalex.org/W2112103497","https://openalex.org/W2120392447","https://openalex.org/W2182414126","https://openalex.org/W2599664950","https://openalex.org/W2798588639","https://openalex.org/W2911865844","https://openalex.org/W3040499212","https://openalex.org/W4205529794","https://openalex.org/W4210848565","https://openalex.org/W4248156396","https://openalex.org/W4300885858","https://openalex.org/W81282799"],"related_works":["https://openalex.org/W4253113110","https://openalex.org/W4251049234","https://openalex.org/W3150713206","https://openalex.org/W2891688494","https://openalex.org/W2280276996","https://openalex.org/W2137780954","https://openalex.org/W2096191306","https://openalex.org/W2096038201","https://openalex.org/W2008876986","https://openalex.org/W1488351281"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,55],"paper":[3],"we":[4,50],"introduce":[5],"a":[6,17,38,43],"new":[7],"natural":[8,33,69],"deduction":[9,34,70],"system":[10,56,71],"for":[11,47,65,82,88],"the":[12,30,62],"logic":[13,23,84],"of":[14,19,21,32],"lattices,":[15],"and":[16,42,49,77,85],"number":[18],"extensions":[20],"lattice":[22,66],"with":[24,36],"different":[25],"negation":[26],"connectives.":[27],"We":[28],"provide":[29],"class":[31],"proofs":[35],"both":[37,74],"standard":[39],"inductive":[40],"definition":[41],"global":[44],"graph-theoretical":[45],"criterion":[46],"correctness,":[48],"show":[51],"how":[52],"normalisation":[53],"in":[54,61],"corresponds":[57],"to":[58],"cut":[59],"elimination":[60],"sequent":[63],"calculus":[64],"logic.":[67,90],"This":[68],"is":[72],"inspired":[73],"by":[75],"Shoesmith":[76],"Smiley's":[78],"multiple":[79],"conclusion":[80],"systems":[81],"classical":[83],"Girard's":[86],"proofnets":[87],"linear":[89]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2134446632","counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-03-19T01:33:04.796964","created_date":"2016-06-24"}