{"id":"https://openalex.org/W4400210530","doi":"https://doi.org/10.1007/978-3-031-63501-4_15","title":"Unification in\u00a0the\u00a0Description Logic $$\\mathcal {ELH}_{\\mathcal {R}^+}$$ Without the\u00a0Top Concept Modulo Cycle-Restricted Ontologies","display_name":"Unification in\u00a0the\u00a0Description Logic $$\\mathcal {ELH}_{\\mathcal {R}^+}$$ Without the\u00a0Top Concept Modulo Cycle-Restricted Ontologies","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4400210530","doi":"https://doi.org/10.1007/978-3-031-63501-4_15"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-63501-4_15","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-63501-4_15","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-63501-4_15.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-63501-4_15.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086254817","display_name":"Franz Baader","orcid":"https://orcid.org/0000-0002-4049-221X"},"institutions":[{"id":"https://openalex.org/I33256026","display_name":"German Research Centre for Artificial Intelligence","ror":"https://ror.org/01ayc5b57","country_code":"DE","type":"funder","lineage":["https://openalex.org/I33256026"]},{"id":"https://openalex.org/I4401726909","display_name":"Center for Scalable Data Analytics and Artificial Intelligence","ror":"https://ror.org/01t4ttr56","country_code":"DE","type":"education","lineage":["https://openalex.org/I4401726909","https://openalex.org/I78650965","https://openalex.org/I926574661"]},{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Franz Baader","raw_affiliation_strings":["Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), Dresden/Leipzig, Germany","Institute of Theoretical Computer Science, TU Dresden, Dresden, Germany"],"raw_orcid":"https://orcid.org/0000-0002-4049-221X","affiliations":[{"raw_affiliation_string":"Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), Dresden/Leipzig, Germany","institution_ids":["https://openalex.org/I33256026","https://openalex.org/I4401726909"]},{"raw_affiliation_string":"Institute of Theoretical Computer Science, TU Dresden, Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033656208","display_name":"Oliver Fern\u00e1ndez Gil","orcid":"https://orcid.org/0000-0002-9458-1701"},"institutions":[{"id":"https://openalex.org/I33256026","display_name":"German Research Centre for Artificial Intelligence","ror":"https://ror.org/01ayc5b57","country_code":"DE","type":"funder","lineage":["https://openalex.org/I33256026"]},{"id":"https://openalex.org/I4401726909","display_name":"Center for Scalable Data Analytics and Artificial Intelligence","ror":"https://ror.org/01t4ttr56","country_code":"DE","type":"education","lineage":["https://openalex.org/I4401726909","https://openalex.org/I78650965","https://openalex.org/I926574661"]},{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Oliver Fern\u00e1ndez Gil","raw_affiliation_strings":["Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), Dresden/Leipzig, Germany","Institute of Theoretical Computer Science, TU Dresden, Dresden, Germany"],"raw_orcid":"https://orcid.org/0000-0002-9458-1701","affiliations":[{"raw_affiliation_string":"Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), Dresden/Leipzig, Germany","institution_ids":["https://openalex.org/I33256026","https://openalex.org/I4401726909"]},{"raw_affiliation_string":"Institute of Theoretical Computer Science, TU Dresden, Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5033656208"],"corresponding_institution_ids":["https://openalex.org/I33256026","https://openalex.org/I4401726909","https://openalex.org/I78650965"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"279","last_page":"297"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10215","display_name":"Semantic Web and Ontologies","score":0.9998999834060669,"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":0.9998999834060669,"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/T11710","display_name":"Biomedical Text Mining and Ontologies","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9945999979972839,"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/unification","display_name":"Unification","score":0.8466985821723938},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7160873413085938},{"id":"https://openalex.org/keywords/ontology","display_name":"Ontology","score":0.6593852043151855},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.6512556672096252},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.6455562114715576},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6039557456970215},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47379228472709656},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.45345067977905273},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.44008007645606995},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3651891350746155},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3465108573436737},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.346047580242157},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34087806940078735},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3281981945037842},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2674531936645508},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14442956447601318},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.10569748282432556},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.08722379803657532}],"concepts":[{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.8466985821723938},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7160873413085938},{"id":"https://openalex.org/C25810664","wikidata":"https://www.wikidata.org/wiki/Q44325","display_name":"Ontology","level":2,"score":0.6593852043151855},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.6512556672096252},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6455562114715576},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6039557456970215},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47379228472709656},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.45345067977905273},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.44008007645606995},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3651891350746155},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3465108573436737},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.346047580242157},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34087806940078735},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3281981945037842},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2674531936645508},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14442956447601318},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.10569748282432556},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.08722379803657532},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-63501-4_15","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-63501-4_15","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-63501-4_15.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-63501-4_15","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-63501-4_15","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-63501-4_15.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.7799999713897705}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4400210530.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W49011482","https://openalex.org/W75191613","https://openalex.org/W196842918","https://openalex.org/W1537167203","https://openalex.org/W1805108069","https://openalex.org/W1982129592","https://openalex.org/W2031848583","https://openalex.org/W2049209348","https://openalex.org/W2083138714","https://openalex.org/W2142835256","https://openalex.org/W2149241959","https://openalex.org/W2163668411","https://openalex.org/W2168686048","https://openalex.org/W2477403571","https://openalex.org/W2986211019","https://openalex.org/W3022449549","https://openalex.org/W3039259551","https://openalex.org/W3099652523","https://openalex.org/W3127358641","https://openalex.org/W3213141443","https://openalex.org/W4244275182","https://openalex.org/W4298304116","https://openalex.org/W4299354379","https://openalex.org/W4299798409","https://openalex.org/W4395056107","https://openalex.org/W6640837398"],"related_works":["https://openalex.org/W2282814833","https://openalex.org/W4298069450","https://openalex.org/W2395121892","https://openalex.org/W2207776881","https://openalex.org/W2752600392","https://openalex.org/W298937333","https://openalex.org/W4299725637","https://openalex.org/W2399897862","https://openalex.org/W2401313042","https://openalex.org/W2569384209"],"abstract_inverted_index":{"Abstract":[0],"Unification":[1],"has":[2,43],"been":[3,44],"introduced":[4],"in":[5,15,25,46,68],"Description":[6],"Logic":[7],"(DL)":[8],"as":[9],"a":[10,85,96,134],"means":[11],"to":[12,57,84,112],"detect":[13],"redundancies":[14],"ontologies.":[16],"In":[17],"particular,":[18],"it":[19,50],"was":[20],"shown":[21],"that":[22,53,114],"testing":[23,130],"unifiability":[24,132],"the":[26,54,62,65,75,88,115,123],"DL":[27],"$$\\mathcal{E}\\mathcal{L}$$":[28],"<mml:math":[29],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[30],"<mml:mrow>":[31],"<mml:mi>E</mml:mi>":[32],"<mml:mi>L</mml:mi>":[33],"</mml:mrow>":[34],"</mml:math>":[35],"is":[36,91,95],"an":[37],"NP-complete":[38],"problem,":[39],"and":[40,105],"this":[41,82],"result":[42,83],"extended":[45],"several":[47],"directions.":[48],"Surprisingly,":[49],"turned":[51],"out":[52],"complexity":[55,124],"increases":[56],"PSpace":[58],"if":[59],"one":[60],"disallows":[61],"use":[63],"of":[64,74,100,103,117,125],"top":[66,89],"concept":[67,69,90,104],"descriptions.":[70],"Motivated":[71],"by":[72],"features":[73],"medical":[76],"ontology":[77,98],"SNOMED":[78],"CT,":[79],"we":[80],"extend":[81],"setting":[86],"where":[87],"disallowed,":[92],"but":[93],"there":[94],"background":[97],"consisting":[99],"restricted":[101],"forms":[102],"role":[106],"inclusion":[107],"axioms.":[108],"We":[109],"are":[110],"able":[111],"show":[113],"presence":[116],"such":[118],"axioms":[119],"does":[120],"not":[121],"increase":[122],"unification":[126],"without":[127],"top,":[128],"i.e.,":[129],"for":[131],"remains":[133],"PSpace-complete":[135],"problem.":[136]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}