{"id":"https://openalex.org/W4205280255","doi":"https://doi.org/10.3233/faia210498","title":"Chapter 17. Logic Tensor Networks: Theory and Applications","display_name":"Chapter 17. Logic Tensor Networks: Theory and Applications","publication_year":2021,"publication_date":"2021-12-22","ids":{"openalex":"https://openalex.org/W4205280255","doi":"https://doi.org/10.3233/faia210498"},"language":"en","primary_location":{"id":"doi:10.3233/faia210498","is_oa":false,"landing_page_url":"https://doi.org/10.3233/faia210498","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"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":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ebooks.iospress.nl/doi/10.3233/FAIA210498","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023894100","display_name":"Luciano Serafini","orcid":"https://orcid.org/0000-0003-4812-1031"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luciano Serafini","raw_affiliation_strings":["FBK, Trento, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FBK, Trento, Italy","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060005929","display_name":"Artur d\u2019Avila Garcez","orcid":"https://orcid.org/0000-0001-7375-9518"},"institutions":[{"id":"https://openalex.org/I180825142","display_name":"City, University of London","ror":"https://ror.org/04489at23","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I180825142"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Artur d\u2019Avila Garcez","raw_affiliation_strings":["City, University of London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"City, University of London, UK","institution_ids":["https://openalex.org/I180825142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083911821","display_name":"Samy Badreddine","orcid":"https://orcid.org/0000-0003-1624-9188"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Samy Badreddine","raw_affiliation_strings":["Sony AI, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sony AI, Japan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077460125","display_name":"Ivan Donadello","orcid":"https://orcid.org/0000-0002-0701-5729"},"institutions":[{"id":"https://openalex.org/I171543936","display_name":"Free University of Bozen-Bolzano","ror":"https://ror.org/012ajp527","country_code":"IT","type":"education","lineage":["https://openalex.org/I171543936"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Ivan Donadello","raw_affiliation_strings":["Free University of Bozen-Bolzano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Free University of Bozen-Bolzano, Italy","institution_ids":["https://openalex.org/I171543936"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071179999","display_name":"Michael Spranger","orcid":"https://orcid.org/0000-0001-9443-7008"},"institutions":[{"id":"https://openalex.org/I4210122684","display_name":"Sony Computer Science Laboratories","ror":"https://ror.org/02nc46417","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210122684"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Michael Spranger","raw_affiliation_strings":["Sony AI, Sony CSL, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sony AI, Sony CSL, Japan","institution_ids":["https://openalex.org/I4210122684"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078515950","display_name":"Federico Bianchi","orcid":"https://orcid.org/0000-0003-0776-361X"},"institutions":[{"id":"https://openalex.org/I71209653","display_name":"Bocconi University","ror":"https://ror.org/05crjpb27","country_code":"IT","type":"education","lineage":["https://openalex.org/I71209653"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Federico Bianchi","raw_affiliation_strings":["Bocconi Univesity, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bocconi Univesity, Milan, Italy","institution_ids":["https://openalex.org/I71209653"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1046,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.81511262,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10215","display_name":"Semantic Web and Ontologies","score":0.9887999892234802,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9887999892234802,"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/T10028","display_name":"Topic Modeling","score":0.9670000076293945,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.949400007724762,"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/computer-science","display_name":"Computer science","score":0.6326594352722168},{"id":"https://openalex.org/keywords/knowledge-representation-and-reasoning","display_name":"Knowledge representation and reasoning","score":0.5646536946296692},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.55189448595047},{"id":"https://openalex.org/keywords/inductive-logic-programming","display_name":"Inductive logic programming","score":0.48144739866256714},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.44163939356803894},{"id":"https://openalex.org/keywords/modalities","display_name":"Modalities","score":0.44159093499183655},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.4232466220855713},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.41097119450569153},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.38553327322006226},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2492128610610962}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6326594352722168},{"id":"https://openalex.org/C161301231","wikidata":"https://www.wikidata.org/wiki/Q3478658","display_name":"Knowledge representation and reasoning","level":2,"score":0.5646536946296692},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.55189448595047},{"id":"https://openalex.org/C2779382394","wikidata":"https://www.wikidata.org/wiki/Q1464197","display_name":"Inductive logic programming","level":2,"score":0.48144739866256714},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.44163939356803894},{"id":"https://openalex.org/C2779903281","wikidata":"https://www.wikidata.org/wiki/Q6888026","display_name":"Modalities","level":2,"score":0.44159093499183655},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.4232466220855713},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.41097119450569153},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.38553327322006226},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2492128610610962},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"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/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3233/faia210498","is_oa":false,"landing_page_url":"https://doi.org/10.3233/faia210498","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"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":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},{"id":"pmh:oai:alma.39UBZ_INST:11290487560001241","is_oa":true,"landing_page_url":"https://ebooks.iospress.nl/doi/10.3233/FAIA210498","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"}],"best_oa_location":{"id":"pmh:oai:alma.39UBZ_INST:11290487560001241","is_oa":true,"landing_page_url":"https://ebooks.iospress.nl/doi/10.3233/FAIA210498","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2978856588","https://openalex.org/W2995623605","https://openalex.org/W2953272728","https://openalex.org/W2185469136","https://openalex.org/W1501498539","https://openalex.org/W1558569658","https://openalex.org/W2468509525","https://openalex.org/W1494464412","https://openalex.org/W2941608206","https://openalex.org/W103453178"],"abstract_inverted_index":{"The":[0,295],"recent":[1,302],"availability":[2],"of":[3,107,115,248,254,299,304,312],"large-scale":[4],"data":[5,8,50,94,122,169,285],"combining":[6,110],"multiple":[7,121],"modalities":[9],"has":[10,24,190,259],"opened":[11],"various":[12],"research":[13],"and":[14,52,56,77,96,117,136,141,165,170,222,241,256,274,276,292,315,323],"commercial":[15],"opportunities":[16],"in":[17,28,199,309],"Artificial":[18],"Intelligence":[19],"(AI).":[20],"Machine":[21],"Learning":[22],"(ML)":[23],"achieved":[25],"important":[26,265],"results":[27,308],"this":[29],"area":[30],"mostly":[31],"by":[32,144],"adopting":[33],"a":[34,158,177,237],"sub-symbolic":[35,46,134,139],"distributed":[36],"representation.":[37],"It":[38,243],"is":[39,62,194],"generally":[40],"accepted":[41],"now":[42],"that":[43,186,193,212],"such":[44,150,185],"purely":[45],"approaches":[47,109],"can":[48],"be":[49],"inefficient":[51],"struggle":[53],"at":[54,80],"extrapolation":[55],"reasoning.":[57,257],"By":[58],"contrast,":[59],"symbolic":[60,82,147,188],"AI":[61,83,100,126,160,266,322,325],"based":[63,69],"on":[64,70,226,250],"rich,":[65],"high-level":[66,146],"representations":[67,135,140],"ideally":[68],"human-readable":[71],"symbols.":[72],"Despite":[73],"being":[74],"more":[75],"explainable":[76],"having":[78],"success":[79],"reasoning,":[81,275],"usually":[84],"struggles":[85],"when":[86],"faced":[87],"with":[88,112,167,182],"incomplete":[89],"knowledge":[90,116,131,227],"or":[91],"inaccurate,":[92],"large":[93],"sets":[95],"combinatorial":[97],"knowledge.":[98,172],"Neurosymbolic":[99],"attempts":[101],"to":[102,128,137,230,263],"benefit":[103],"from":[104,120],"the":[105,200,219,232,246,300,310,317],"strengths":[106],"both":[108],"reasoning":[111,166,291],"complex":[113],"representation":[114],"efficient":[118,133],"learning":[119,143,151,164,253,273],"modalities.":[123],"Hence,":[124],"neurosymbolic":[125,159,321],"seeks":[127],"ground":[129,231],"rich":[130,168],"into":[132,209,236],"explain":[138],"deep":[142],"offering":[145],"descriptions":[148],"for":[149,162,282,320],"systems.":[152],"Logic":[153,207],"Tensor":[154],"Networks":[155],"(LTN)":[156],"are":[157],"system":[161],"querying,":[163],"abstract":[171],"LTN":[173,204,220,249,258,281,305],"introduces":[174],"Real":[175,206],"Logic,":[176],"fully":[178],"differentiable":[179],"first-order":[180],"language":[181],"concrete":[183,238],"semantics":[184],"every":[187],"expression":[189],"an":[191],"interpretation":[192,239],"grounded":[195],"onto":[196],"real":[197],"numbers":[198],"domain.":[201],"In":[202],"particular,":[203],"converts":[205],"formulas":[208],"computational":[210],"graphs":[211],"enable":[213],"gradient-based":[214],"optimization.":[215],"This":[216],"chapter":[217,296],"presents":[218,297],"framework":[221],"illustrates":[223],"its":[224],"use":[225,247,280],"completion":[228],"tasks":[229],"relational":[233],"predicates":[234],"(symbols)":[235],"(vectors":[240],"tensors).":[242],"then":[244],"investigates":[245],"semi-supervised":[251,287],"learning,":[252,278,288,290],"embeddings":[255],"been":[260],"applied":[261],"recently":[262],"many":[264],"tasks,":[267],"including":[268],"semantic":[269],"image":[270],"interpretation,":[271],"ontology":[272],"reinforcement":[277],"which":[279],"supervised":[283],"classification,":[284],"clustering,":[286],"embedding":[289],"query":[293],"answering.":[294],"some":[298],"main":[301],"applications":[303],"before":[306],"analyzing":[307],"context":[311],"related":[313],"work":[314],"discussing":[316],"next":[318],"steps":[319],"LTN-based":[324],"models.":[326]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
