{"id":"https://openalex.org/W2912858786","doi":"https://doi.org/10.29007/8l5l","title":"Scheme representation for first-order logic","display_name":"Scheme representation for first-order logic","publication_year":2018,"publication_date":"2018-01-23","ids":{"openalex":"https://openalex.org/W2912858786","doi":"https://doi.org/10.29007/8l5l","mag":"2912858786"},"language":"en","primary_location":{"id":"doi:10.29007/8l5l","is_oa":true,"landing_page_url":"https://doi.org/10.29007/8l5l","pdf_url":"https://easychair.org/publications/open/dRJ","source":{"id":"https://openalex.org/S4220651395","display_name":"EPiC series in computing","issn_l":"2398-7340","issn":["2398-7340"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EPiC Series in Computing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://easychair.org/publications/open/dRJ","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048294977","display_name":"Steve Awodey","orcid":"https://orcid.org/0000-0001-9005-179X"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steve Awodey","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, Pennsylvania, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, Pennsylvania, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030897707","display_name":"Spencer Breiner","orcid":"https://orcid.org/0000-0001-5400-1349"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Spencer Breiner","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, Pennsylvania, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, Pennsylvania, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.8031,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.75892857,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"25","issue":null,"first_page":"10","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sheaf","display_name":"Sheaf","score":0.7859489321708679},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6405056118965149},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6070436239242554},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.566905677318573},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5377393364906311},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.530061662197113},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5289145708084106},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4676627218723297},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.43944239616394043},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32446569204330444},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28230708837509155}],"concepts":[{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.7859489321708679},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6405056118965149},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6070436239242554},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.566905677318573},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5377393364906311},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.530061662197113},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5289145708084106},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4676627218723297},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.43944239616394043},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32446569204330444},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28230708837509155},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.29007/8l5l","is_oa":true,"landing_page_url":"https://doi.org/10.29007/8l5l","pdf_url":"https://easychair.org/publications/open/dRJ","source":{"id":"https://openalex.org/S4220651395","display_name":"EPiC series in computing","issn_l":"2398-7340","issn":["2398-7340"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EPiC Series in Computing","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.29007/8l5l","is_oa":true,"landing_page_url":"https://doi.org/10.29007/8l5l","pdf_url":"https://easychair.org/publications/open/dRJ","source":{"id":"https://openalex.org/S4220651395","display_name":"EPiC series in computing","issn_l":"2398-7340","issn":["2398-7340"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EPiC Series in Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2912858786.pdf","grobid_xml":"https://content.openalex.org/works/W2912858786.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W14582567","https://openalex.org/W1481038699","https://openalex.org/W1724982428","https://openalex.org/W1982346842","https://openalex.org/W1994467436","https://openalex.org/W2011659388","https://openalex.org/W2131112857","https://openalex.org/W2144927799","https://openalex.org/W2401027626","https://openalex.org/W6637570721"],"related_works":["https://openalex.org/W2159266974","https://openalex.org/W1975289146","https://openalex.org/W1983407640","https://openalex.org/W2105887828","https://openalex.org/W2122599759","https://openalex.org/W3023070374","https://openalex.org/W1529494625","https://openalex.org/W2342017063","https://openalex.org/W2351578128","https://openalex.org/W2950460772"],"abstract_inverted_index":{"My":[0],"research":[1],"concerns":[2],"a":[3,28,33,45,53,63,75],"construction":[4],"of":[5,77,83,87],"\"logical":[6],"schemes,\"":[7],"geometric":[8],"entities":[9],"which":[10,80],"represent":[11,22],"logical":[12,65,78],"theories":[13],"in":[14,38,62],"much":[15],"the":[16,39,57,84],"same":[17],"way":[18],"that":[19],"algebraic":[20,40,88],"schemes":[21,79],"rings.":[23],"These":[24],"involve":[25],"two":[26],"components:":[27],"semantic":[29],"spectral":[30],"space":[31],"and":[32,56],"syntactic":[34],"structure":[35,58],"sheaf.":[36],"As":[37],"case,":[41],"we":[42,71],"can":[43,72],"recover":[44],"theory":[46],"from":[47],"its":[48],"scheme":[49],"representation":[50],"(up":[51],"to":[52],"conservative":[54],"completion)":[55],"sheaf":[59],"is":[60],"local":[61],"certain":[64],"sense.":[66],"From":[67],"these":[68],"ane":[69],"pieces":[70],"build":[73],"up":[74],"2-category":[76],"share":[81],"some":[82],"nice":[85],"properties":[86],"schemes.":[89]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}