{"id":"https://openalex.org/W2942867061","doi":"https://doi.org/10.23638/lmcs-16(1:13)2020","title":"Overlap Algebras: a Constructive Look at Complete Boolean Algebras","display_name":"Overlap Algebras: a Constructive Look at Complete Boolean Algebras","publication_year":2020,"publication_date":"2020-02-13","ids":{"openalex":"https://openalex.org/W2942867061","doi":"https://doi.org/10.23638/lmcs-16(1:13)2020","mag":"2942867061"},"language":"en","primary_location":{"id":"doi:10.23638/lmcs-16(1:13)2020","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-16(1:13)2020","pdf_url":"https://lmcs.episciences.org/6096/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","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/6096/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033738872","display_name":"Francesco Ciraulo","orcid":"https://orcid.org/0000-0002-4957-4799"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Francesco Ciraulo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039563766","display_name":"Michele Contente","orcid":"https://orcid.org/0000-0002-6433-0127"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michele Contente","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2536,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.57619067,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"Volume 16, Issue 1","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9904999732971191,"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"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9904999732971191,"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"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9099000096321106,"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":0.9028000235557556,"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/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.8153196573257446},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.8114737272262573},{"id":"https://openalex.org/keywords/boolean-algebras-canonically-defined","display_name":"Boolean algebras canonically defined","score":0.7376220226287842},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7078602910041809},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6837692856788635},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.661029577255249},{"id":"https://openalex.org/keywords/joins","display_name":"Joins","score":0.613602876663208},{"id":"https://openalex.org/keywords/free-boolean-algebra","display_name":"Free Boolean algebra","score":0.5775244235992432},{"id":"https://openalex.org/keywords/interior-algebra","display_name":"Interior algebra","score":0.5698236227035522},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.568790078163147},{"id":"https://openalex.org/keywords/stones-representation-theorem-for-boolean-algebras","display_name":"Stone's representation theorem for Boolean algebras","score":0.5466275215148926},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4282826781272888},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41172122955322266},{"id":"https://openalex.org/keywords/heyting-algebra","display_name":"Heyting algebra","score":0.41032448410987854},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4030234217643738},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37424808740615845},{"id":"https://openalex.org/keywords/jordan-algebra","display_name":"Jordan algebra","score":0.20028093457221985},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.1717890202999115},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15712043642997742}],"concepts":[{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.8153196573257446},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.8114737272262573},{"id":"https://openalex.org/C45503250","wikidata":"https://www.wikidata.org/wiki/Q4943350","display_name":"Boolean algebras canonically defined","level":5,"score":0.7376220226287842},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7078602910041809},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6837692856788635},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.661029577255249},{"id":"https://openalex.org/C2778692605","wikidata":"https://www.wikidata.org/wiki/Q4041866","display_name":"Joins","level":2,"score":0.613602876663208},{"id":"https://openalex.org/C188159880","wikidata":"https://www.wikidata.org/wiki/Q5499761","display_name":"Free Boolean algebra","level":5,"score":0.5775244235992432},{"id":"https://openalex.org/C203254541","wikidata":"https://www.wikidata.org/wiki/Q10894825","display_name":"Interior algebra","level":5,"score":0.5698236227035522},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.568790078163147},{"id":"https://openalex.org/C10021369","wikidata":"https://www.wikidata.org/wiki/Q1166774","display_name":"Stone's representation theorem for Boolean algebras","level":5,"score":0.5466275215148926},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4282826781272888},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41172122955322266},{"id":"https://openalex.org/C187062830","wikidata":"https://www.wikidata.org/wiki/Q1617044","display_name":"Heyting algebra","level":3,"score":0.41032448410987854},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4030234217643738},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37424808740615845},{"id":"https://openalex.org/C100376341","wikidata":"https://www.wikidata.org/wiki/Q649977","display_name":"Jordan algebra","level":4,"score":0.20028093457221985},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.1717890202999115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15712043642997742},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.23638/lmcs-16(1:13)2020","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-16(1:13)2020","pdf_url":"https://lmcs.episciences.org/6096/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:1904.13320","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.13320","pdf_url":"https://arxiv.org/pdf/1904.13320","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:www.research.unipd.it:11577/3332954","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1904.13320v3","pdf_url":"https://lmcs.episciences.org/6096","source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1904.13320","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1904.13320","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.23638/lmcs-16(1:13)2020","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-16(1:13)2020","pdf_url":"https://lmcs.episciences.org/6096/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":[{"id":"https://openalex.org/G434337789","display_name":null,"funder_award_id":"HORIZON2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5916636757","display_name":"Computing with Infinite Data","funder_award_id":"731143","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2942867061.pdf","grobid_xml":"https://content.openalex.org/works/W2942867061.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1987007120","https://openalex.org/W1992205482","https://openalex.org/W2011659388","https://openalex.org/W2047480683","https://openalex.org/W2060621887","https://openalex.org/W2264357731","https://openalex.org/W2487483580"],"related_works":["https://openalex.org/W2064128553","https://openalex.org/W2951697398","https://openalex.org/W4300190062","https://openalex.org/W2581929395","https://openalex.org/W2314217485","https://openalex.org/W4255268210","https://openalex.org/W1997468345","https://openalex.org/W4247131462","https://openalex.org/W76615774","https://openalex.org/W1994149745"],"abstract_inverted_index":{"The":[0],"notion":[1,30],"of":[2,23,25,31,40,60,66,69,107,120,143,151],"a":[3,26,41,84,87,96],"complete":[4,42,121],"Boolean":[5,43,122,147],"algebra,":[6,34,44],"although":[7,35],"completely":[8],"legitimate":[9],"in":[10],"constructive":[11,141],"mathematics,":[12],"fails":[13],"to":[14,38,104],"capture":[15],"some":[16,76,144],"natural":[17,49],"structures":[18,50],"such":[19],"as":[20,51,63],"the":[21,58,67,105,117],"lattice":[22],"subsets":[24],"given":[27],"set.":[28],"Sambin's":[29],"an":[32,64],"overlap":[33,61,127],"classically":[36],"equivalent":[37],"that":[39],"has":[45],"powersets":[46],"and":[47,71,73,81,131],"other":[48],"instances.":[52],"In":[53],"this":[54,93,115],"paper":[55],"we":[56,74,102,125],"study":[57],"category":[59,68,119],"algebras":[62,128],"extension":[65],"sets":[70],"relations,":[72],"establish":[75],"basic":[77],"facts":[78],"about":[79,146],"mono-epi-isomorphisms":[80],"(co)limits;":[82],"here":[83],"morphism":[85],"is":[86,94,116],"symmetrizable":[88],"function":[89,97],"(with":[90],"classical":[91],"logic":[92],"just":[95],"which":[98,109],"preserves":[99],"joins).":[100],"Then":[101],"specialize":[103],"case":[106],"morphisms":[108,133],"preserve":[110],"also":[111],"finite":[112],"meets:":[113],"classically,":[114],"usual":[118],"algebras.":[123],"Finally,":[124],"connect":[126],"with":[129,134],"locales,":[130,138],"their":[132],"open":[135],"maps":[136],"between":[137],"thus":[139],"obtaining":[140],"versions":[142],"results":[145],"locales.":[148],"Comment:":[149],"Postproceedings":[150],"CCC2018:":[152],"Continuity,":[153],"Computability,":[154],"Constructivity.":[155],"Faro,":[156],"Portugal,":[157],"24-28":[158],"Sep":[159],"2018":[160]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}