{"id":"https://openalex.org/W2011879117","doi":"https://doi.org/10.1093/logcom/exp017","title":"A Compact [0,1]-valued First-order Lukasiewicz Logic with Identity on Hilbert Space","display_name":"A Compact [0,1]-valued First-order Lukasiewicz Logic with Identity on Hilbert Space","publication_year":2009,"publication_date":"2009-03-13","ids":{"openalex":"https://openalex.org/W2011879117","doi":"https://doi.org/10.1093/logcom/exp017","mag":"2011879117"},"language":"en","primary_location":{"id":"doi:10.1093/logcom/exp017","is_oa":false,"landing_page_url":"https://doi.org/10.1093/logcom/exp017","pdf_url":null,"source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","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/A5069739656","display_name":"Daniele Mundici","orcid":"https://orcid.org/0000-0002-6779-3362"},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"D. Mundici","raw_affiliation_strings":["Department of Mathematics, \u2018Ulisse Dini\u2019, University of Florence, Viale Morgagni 67/A, I-50134 Florence, Italy.E-mail: mundici@math.unifi.it","Department of Mathematics, \u2018Ulisse Dini\u2019, University of Florence, Viale Morgagni 67/A, I-50134 Florence, Italy.E-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, \u2018Ulisse Dini\u2019, University of Florence, Viale Morgagni 67/A, I-50134 Florence, Italy.E-mail: mundici@math.unifi.it","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Department of Mathematics, \u2018Ulisse Dini\u2019, University of Florence, Viale Morgagni 67/A, I-50134 Florence, Italy.E-mail:","institution_ids":["https://openalex.org/I45084792"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069739656"],"corresponding_institution_ids":["https://openalex.org/I45084792"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.3428,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.59226622,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"21","issue":"3","first_page":"509","last_page":"525"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9998999834060669,"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":0.9998999834060669,"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":0.996399998664856,"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/T11567","display_name":"semigroups and automata theory","score":0.9919000267982483,"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/mathematics","display_name":"Mathematics","score":0.7991579174995422},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6569938063621521},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.6432098150253296},{"id":"https://openalex.org/keywords/\u0142ukasiewicz-logic","display_name":"\u0141ukasiewicz logic","score":0.6426581144332886},{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.57433021068573},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.47842031717300415},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.46527478098869324},{"id":"https://openalex.org/keywords/linear-span","display_name":"Linear span","score":0.4538317322731018},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4447835683822632},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4360429346561432},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.42680424451828003},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3623310923576355},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3613601326942444},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.32175692915916443},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0948193371295929}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7991579174995422},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6569938063621521},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.6432098150253296},{"id":"https://openalex.org/C206321295","wikidata":"https://www.wikidata.org/wiki/Q8080919","display_name":"\u0141ukasiewicz logic","level":5,"score":0.6426581144332886},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.57433021068573},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.47842031717300415},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.46527478098869324},{"id":"https://openalex.org/C133226019","wikidata":"https://www.wikidata.org/wiki/Q209812","display_name":"Linear span","level":2,"score":0.4538317322731018},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4447835683822632},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4360429346561432},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.42680424451828003},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3623310923576355},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3613601326942444},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.32175692915916443},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0948193371295929},{"id":"https://openalex.org/C144760519","wikidata":"https://www.wikidata.org/wiki/Q839490","display_name":"Substructural logic","level":4,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1093/logcom/exp017","is_oa":false,"landing_page_url":"https://doi.org/10.1093/logcom/exp017","pdf_url":null,"source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},{"id":"pmh:oai:flore.unifi.it:2158/403846","is_oa":false,"landing_page_url":"http://hdl.handle.net/2158/403846","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.6800000071525574,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W179694669","https://openalex.org/W933639427","https://openalex.org/W1556760457","https://openalex.org/W1566552629","https://openalex.org/W1992818631","https://openalex.org/W2011526622","https://openalex.org/W2110182592","https://openalex.org/W2156452084","https://openalex.org/W2612686320","https://openalex.org/W2799061192"],"related_works":["https://openalex.org/W4229066371","https://openalex.org/W4284710897","https://openalex.org/W4385766541","https://openalex.org/W88232665","https://openalex.org/W637989598","https://openalex.org/W2952610483","https://openalex.org/W1566013760","https://openalex.org/W4382490866","https://openalex.org/W4299522860","https://openalex.org/W193449051"],"abstract_inverted_index":{"By":[0],"an":[1,89],"MV-set,":[2],"we":[3,66,94],"understand":[4],"a":[5,11,17,68],"pair":[6],"(E,X)":[7],"where":[8],"X":[9,27,87],"is":[10,28,47,79,88],"set":[12,75],"of":[13,26,51,76,92],"unit":[14],"vectors":[15],"in":[16,30],"Hilbert":[18],"space":[19],"E":[20,93],"such":[21],"that":[22],"the":[23,48,83,110,119],"linear":[24],"span":[25],"dense":[29],"E,":[31],"and":[32,53,58,61,104,118,126],"\u3008v,w\u3009":[33,44],"\u2265":[34],"0":[35],"for":[36,114,123],"all":[37],"v,w":[38],"\u2208":[39,45],"X.":[40],"The":[41],"scalar":[42],"product":[43],"[0,1]":[46],"identity":[49],"degree":[50],"v":[52],"w.":[54],"Building":[55],"on":[56,64],"MV-sets":[57],"continuous":[59],"functions":[60,103],"relations":[62],"defined":[63],"them,":[65],"construct":[67],"compact":[69],"[0,1]-valued":[70],"first-order":[71,98],"\u0141ukasiewicz":[72],"logic,":[73],"whose":[74],"unsatisfiable":[77],"formulas":[78],"recursively":[80],"enumerable.":[81],"In":[82],"particular":[84],"case":[85],"when":[86],"orthonormal":[90],"basis":[91],"recover":[95],"classical":[96],"Skolem":[97],"logic":[99],"with":[100],"identity,":[101],"constants,":[102],"relations.":[105],"Our":[106],"main":[107],"tools":[108],"are":[109],"Kolmogorov":[111],"dilation":[112],"theorem":[113],"positive":[115],"semidefinite":[116],"kernels,":[117],"Tarski\u2013Seidenberg":[120],"decision":[121],"method":[122],"elementary":[124],"algebra":[125],"geometry.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
