{"id":"https://openalex.org/W4255223281","doi":"https://doi.org/10.3233/fi-2016-1449","title":"Tiered Objects","display_name":"Tiered Objects","publication_year":2016,"publication_date":"2016-12-24","ids":{"openalex":"https://openalex.org/W4255223281","doi":"https://doi.org/10.3233/fi-2016-1449"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2016-1449","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2016-1449","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2318/1633801","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010809367","display_name":"Fabio Alessi","orcid":null},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]},{"id":"https://openalex.org/I55143463","display_name":"University of Turin","ror":"https://ror.org/048tbm396","country_code":"IT","type":"education","lineage":["https://openalex.org/I55143463"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Fabio Alessi","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 di Torino corso Svizzera 185 I-10149 Torino, Italy","Dipartimento di Scienze Matematiche Informatiche e Fisiche Universit\u00e0 di Udine via delle Scienze 206, I-33100 Udine, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 di Torino corso Svizzera 185 I-10149 Torino, Italy","institution_ids":["https://openalex.org/I55143463"]},{"raw_affiliation_string":"Dipartimento di Scienze Matematiche Informatiche e Fisiche Universit\u00e0 di Udine via delle Scienze 206, I-33100 Udine, Italy","institution_ids":["https://openalex.org/I129043915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024664392","display_name":"Felice Cardone","orcid":"https://orcid.org/0000-0002-4841-614X"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]},{"id":"https://openalex.org/I55143463","display_name":"University of Turin","ror":"https://ror.org/048tbm396","country_code":"IT","type":"education","lineage":["https://openalex.org/I55143463"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Felice Cardone","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 di Torino corso Svizzera 185 I-10149 Torino, Italy","Dipartimento di Scienze Matematiche Informatiche e Fisiche Universit\u00e0 di Udine via delle Scienze 206, I-33100 Udine, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 di Torino corso Svizzera 185 I-10149 Torino, Italy","institution_ids":["https://openalex.org/I55143463"]},{"raw_affiliation_string":"Dipartimento di Scienze Matematiche Informatiche e Fisiche Universit\u00e0 di Udine via delle Scienze 206, I-33100 Udine, Italy","institution_ids":["https://openalex.org/I129043915"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010809367"],"corresponding_institution_ids":["https://openalex.org/I129043915","https://openalex.org/I55143463"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24964393,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"149","issue":"3","first_page":"263","last_page":"295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9983999729156494,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9972000122070312,"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/mathematics","display_name":"Mathematics","score":0.6651803255081177},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5288687348365784},{"id":"https://openalex.org/keywords/heyting-algebra","display_name":"Heyting algebra","score":0.5203127861022949},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5008294582366943},{"id":"https://openalex.org/keywords/sheaf","display_name":"Sheaf","score":0.4934800863265991},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4717584252357483},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4296048879623413},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37274399399757385},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3512917459011078},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28086191415786743},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1664150059223175},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.14730477333068848}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6651803255081177},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5288687348365784},{"id":"https://openalex.org/C187062830","wikidata":"https://www.wikidata.org/wiki/Q1617044","display_name":"Heyting algebra","level":3,"score":0.5203127861022949},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5008294582366943},{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.4934800863265991},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4717584252357483},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4296048879623413},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37274399399757385},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3512917459011078},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28086191415786743},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1664150059223175},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.14730477333068848}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3233/fi-2016-1449","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2016-1449","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:iris.unito.it:2318/1633801","is_oa":true,"landing_page_url":"http://hdl.handle.net/2318/1633801","pdf_url":"http://hdl.handle.net/2318/1633801","source":{"id":"https://openalex.org/S4306400637","display_name":"Institutional Research Information System University of Turin (University of Turin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I55143463","host_organization_name":"University of Turin","host_organization_lineage":["https://openalex.org/I55143463"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:air.uniud.it:11390/1134859","is_oa":true,"landing_page_url":"http://hdl.handle.net/11390/1134859","pdf_url":null,"source":{"id":"https://openalex.org/S4306401163","display_name":"Institutional Research Information System (University of Udine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129043915","host_organization_name":"University of Udine","host_organization_lineage":["https://openalex.org/I129043915"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:iris.unito.it:2318/1633801","is_oa":true,"landing_page_url":"http://hdl.handle.net/2318/1633801","pdf_url":"http://hdl.handle.net/2318/1633801","source":{"id":"https://openalex.org/S4306400637","display_name":"Institutional Research Information System University of Turin (University of Turin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I55143463","host_organization_name":"University of Turin","host_organization_lineage":["https://openalex.org/I55143463"],"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":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4255223281.pdf","grobid_xml":"https://content.openalex.org/works/W4255223281.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W46845843","https://openalex.org/W1490282072","https://openalex.org/W1491165055","https://openalex.org/W1511668635","https://openalex.org/W1563160544","https://openalex.org/W1576579629","https://openalex.org/W1589260337","https://openalex.org/W1719974439","https://openalex.org/W1970249071","https://openalex.org/W1997422577","https://openalex.org/W1998875295","https://openalex.org/W2011825885","https://openalex.org/W2019066753","https://openalex.org/W2023739237","https://openalex.org/W2033537467","https://openalex.org/W2040810354","https://openalex.org/W2068112097","https://openalex.org/W2079452454","https://openalex.org/W2081620669","https://openalex.org/W2110907326","https://openalex.org/W2116542587","https://openalex.org/W2127110013","https://openalex.org/W2138608576","https://openalex.org/W2165563109","https://openalex.org/W2574983198","https://openalex.org/W2912407587","https://openalex.org/W2952652756","https://openalex.org/W4235871102"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2041295491","https://openalex.org/W2600895957","https://openalex.org/W2771140321","https://openalex.org/W2264018172","https://openalex.org/W2109494992","https://openalex.org/W3122456069","https://openalex.org/W4381714206","https://openalex.org/W2124331519","https://openalex.org/W2389970330"],"abstract_inverted_index":{"We":[0,47],"investigate":[1],"the":[2,17,65],"foundations":[3],"of":[4,12,20,31,36,38,58,62,64,67],"reasoning":[5],"over":[6],"infinite":[7],"data":[8],"structures":[9,14],"by":[10],"means":[11],"set-theoretical":[13],"arising":[15],"in":[16],"sheaf-theoretic":[18],"semantics":[19],"higher-order":[21],"intuitionistic":[22],"logic.":[23],"Our":[24],"approach":[25],"focuses":[26],"on":[27],"a":[28,43,59,77,82],"natural":[29],"notion":[30],"tiering":[32],"involving":[33],"an":[34],"operation":[35],"restriction":[37],"elements":[39],"to":[40,52],"levels":[41],"forming":[42],"complete":[44],"Heyting":[45],"algebra.":[46],"relate":[48],"these":[49],"tiered":[50,87],"objects":[51],"final":[53],"coalgebras":[54],"and":[55,69,73],"initial":[56],"algebras":[57],"wide":[60],"class":[61],"endofunctors":[63],"category":[66],"sets,":[68],"study":[70],"their":[71],"order":[72],"convergence":[74],"properties.":[75],"As":[76],"sample":[78],"application,":[79],"we":[80],"derive":[81],"general":[83],"proof":[84],"principle":[85],"for":[86],"objects.":[88]},"counts_by_year":[],"updated_date":"2026-05-02T06:04:40.494371","created_date":"2022-05-12T00:00:00"}