{"id":"https://openalex.org/W2084199598","doi":"https://doi.org/10.1016/s1571-0661(04)80613-3","title":"Using DAG Transformations to Verify Euler/Venn Homogeneous and Euler/Venn FOL Heterogeneous Rules of Inference","display_name":"Using DAG Transformations to Verify Euler/Venn Homogeneous and Euler/Venn FOL Heterogeneous Rules of Inference","publication_year":2003,"publication_date":"2003-02-01","ids":{"openalex":"https://openalex.org/W2084199598","doi":"https://doi.org/10.1016/s1571-0661(04)80613-3","mag":"2084199598"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(04)80613-3","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80613-3","pdf_url":"https://www.sciencedirect.com/science/article/pii/S1571066104806133/pdf","source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.sciencedirect.com/science/article/pii/S1571066104806133/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072416359","display_name":"Nik Swoboda","orcid":"https://orcid.org/0000-0002-3095-3115"},"institutions":[{"id":"https://openalex.org/I4210104143","display_name":"Advanced Telecommunications Research Institute International","ror":"https://ror.org/01pe1d703","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210104143"]},{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES","JP"],"is_corresponding":true,"raw_author_name":"Nik Swoboda","raw_affiliation_strings":["Media Information Science Labs, Advanced Telecommunications Research Institute, Seika, Kyoto, Japan","Departamento de Inteligencia Artificial, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain and ATR Media Information Science Labs, Kyoto, Japan#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Media Information Science Labs, Advanced Telecommunications Research Institute, Seika, Kyoto, Japan","institution_ids":["https://openalex.org/I4210104143"]},{"raw_affiliation_string":"Departamento de Inteligencia Artificial, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain and ATR Media Information Science Labs, Kyoto, Japan#TAB#","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070038296","display_name":"Gerard Allwein","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gerard Allwein","raw_affiliation_strings":["Department of Computer Science, Indiana University, Bloomington, IN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Indiana University, Bloomington, IN, USA","institution_ids":["https://openalex.org/I4210119109"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070038296","https://openalex.org/A5072416359"],"corresponding_institution_ids":["https://openalex.org/I4210104143","https://openalex.org/I4210119109","https://openalex.org/I88060688"],"apc_list":null,"apc_paid":null,"fwci":1.0959,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.78297842,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"72","issue":"3","first_page":"78","last_page":"92"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9997000098228455,"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/T10142","display_name":"Formal Methods in Verification","score":0.9997000098228455,"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/T11450","display_name":"Model-Driven Software Engineering Techniques","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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":0.9959999918937683,"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/venn-diagram","display_name":"Venn diagram","score":0.9944809675216675},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7524663209915161},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.621497631072998},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.6080159544944763},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5566587448120117},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5372006893157959},{"id":"https://openalex.org/keywords/rule-of-inference","display_name":"Rule of inference","score":0.4345114529132843},{"id":"https://openalex.org/keywords/directed-acyclic-graph","display_name":"Directed acyclic graph","score":0.43182095885276794},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4012604355812073},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34682726860046387},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3228432536125183},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2449837625026703},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18886730074882507}],"concepts":[{"id":"https://openalex.org/C55508974","wikidata":"https://www.wikidata.org/wiki/Q190763","display_name":"Venn diagram","level":2,"score":0.9944809675216675},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7524663209915161},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.621497631072998},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.6080159544944763},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5566587448120117},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5372006893157959},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.4345114529132843},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.43182095885276794},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4012604355812073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34682726860046387},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3228432536125183},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2449837625026703},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18886730074882507},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s1571-0661(04)80613-3","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80613-3","pdf_url":"https://www.sciencedirect.com/science/article/pii/S1571066104806133/pdf","source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(04)80613-3","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80613-3","pdf_url":"https://www.sciencedirect.com/science/article/pii/S1571066104806133/pdf","source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2084199598.pdf","grobid_xml":"https://content.openalex.org/works/W2084199598.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W360295174","https://openalex.org/W579321050","https://openalex.org/W1489784679","https://openalex.org/W1494153154","https://openalex.org/W1538565162","https://openalex.org/W1553791847","https://openalex.org/W1571636511","https://openalex.org/W1576918130","https://openalex.org/W1592652287","https://openalex.org/W1603641563","https://openalex.org/W1998889043","https://openalex.org/W2030297824","https://openalex.org/W2138741404","https://openalex.org/W6629066213","https://openalex.org/W6629672030","https://openalex.org/W6680393978"],"related_works":["https://openalex.org/W4306970587","https://openalex.org/W1497899451","https://openalex.org/W4256478115","https://openalex.org/W2338867480","https://openalex.org/W2744696476","https://openalex.org/W3156165154","https://openalex.org/W3100271225","https://openalex.org/W1517268357","https://openalex.org/W1616708177","https://openalex.org/W76754608"],"abstract_inverted_index":{"In":[0,73],"this":[1],"paper":[2],"we":[3,78],"will":[4,79,108],"present":[5],"a":[6,27,95],"graph-transformation":[7],"based":[8,114],"method":[9,96],"for":[10,97],"the":[11,74,82,99],"verification":[12],"of":[13,30,55,84,101],"heterogeneous":[14,102],"first":[15],"order":[16],"logic":[17],"(FOL)":[18],"and":[19,104],"Euler/Venn":[20,40,50,64,92,103],"proofs.":[21,93],"It":[22],"has":[23],"been":[24],"shown":[25],"that":[26,111],"special":[28],"collection":[29],"directed":[31],"acyclic":[32],"graphs":[33],"(DAGs)":[34],"can":[35,52,66,87],"be":[36,53,67,88,109],"used":[37,89],"interchangeably":[38],"with":[39,58],"diagrams":[41,51,65],"in":[42],"reasoning":[43,106],"processes":[44],"[4].":[45],"Thus,":[46],"proofs":[47,57],"which":[48],"include":[49],"thought":[54],"as":[56,69],"DAGs":[59],"where":[60],"steps":[61],"involving":[62],"only":[63],"treated":[68],"particular":[70],"DAG":[71,116],"transformations.":[72,117],"work":[75],"reported":[76],"here,":[77],"show":[80],"how":[81],"characterization":[83],"these":[85],"manipulations":[86],"to":[90],"verify":[91],"Also,":[94],"verifying":[98],"use":[100],"FOL":[105],"rules":[107],"presented":[110],"is":[112],"also":[113],"upon":[115]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}