{"id":"https://openalex.org/W1999129624","doi":"https://doi.org/10.1016/s1571-0661(05)01181-3","title":"Algorithms for Equality and Unification in the Presence of Notational Definitions","display_name":"Algorithms for Equality and Unification in the Presence of Notational Definitions","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1999129624","doi":"https://doi.org/10.1016/s1571-0661(05)01181-3","mag":"1999129624"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(05)01181-3","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)01181-3","pdf_url":null,"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://doi.org/10.1016/s1571-0661(05)01181-3","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021476649","display_name":"Frank Pfenning","orcid":"https://orcid.org/0000-0002-8279-5817"},"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":true,"raw_author_name":"Frank Pfenning","raw_affiliation_strings":["Carnegie Mellon University, School of Computer Science","Carnegie Mellon University,School of Computer Science"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, School of Computer Science","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon University,School of Computer Science","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113220543","display_name":"Carsten Sch\u00fcrmann","orcid":"https://orcid.org/0000-0003-4793-0099"},"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":true,"raw_author_name":"Carsten Sch\u00fcrmann","raw_affiliation_strings":["Carnegie Mellon University, School of Computer Science","Carnegie Mellon University,School of Computer Science"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, School of Computer Science","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon University,School of Computer Science","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021476649","https://openalex.org/A5113220543"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.11536245,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"17","issue":null,"first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","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/T10126","display_name":"Logic, programming, and type systems","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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9986000061035156,"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/T10142","display_name":"Formal Methods in Verification","score":0.9976000189781189,"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/unification","display_name":"Unification","score":0.9474446177482605},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.7290377616882324},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.506686270236969},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49909234046936035},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.44748079776763916},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4267711043357849},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4054799973964691},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.39353978633880615},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35644209384918213},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2858136296272278},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14293807744979858}],"concepts":[{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.9474446177482605},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.7290377616882324},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.506686270236969},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49909234046936035},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.44748079776763916},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4267711043357849},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4054799973964691},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.39353978633880615},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35644209384918213},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2858136296272278},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14293807744979858},{"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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s1571-0661(05)01181-3","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)01181-3","pdf_url":null,"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(05)01181-3","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)01181-3","pdf_url":null,"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":[{"display_name":"Reduced inequalities","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W171073024","https://openalex.org/W1534850143","https://openalex.org/W1560253649","https://openalex.org/W1568557936","https://openalex.org/W1569569047","https://openalex.org/W1974190112","https://openalex.org/W1986487716","https://openalex.org/W1990946582","https://openalex.org/W2034676877","https://openalex.org/W2059799630","https://openalex.org/W2075352622","https://openalex.org/W2100758996","https://openalex.org/W2115023762","https://openalex.org/W2154008991","https://openalex.org/W2586148739","https://openalex.org/W4233812427","https://openalex.org/W4236371313"],"related_works":["https://openalex.org/W2367630557","https://openalex.org/W101666983","https://openalex.org/W2183792531","https://openalex.org/W2595286499","https://openalex.org/W2471908688","https://openalex.org/W1845283042","https://openalex.org/W2616882931","https://openalex.org/W2115512867","https://openalex.org/W4231718283","https://openalex.org/W1481154196"],"abstract_inverted_index":{"Notational":[0],"definitions":[1,37],"are":[2,8],"pervasive":[3],"in":[4,11,42],"mathematical":[5],"practic":[6],"and":[7,29],"therefore":[9],"supported":[10],"must":[12],"automated":[13],"theorem":[14],"proving":[15],"systems.":[16],"In":[17],"this":[18],"paper":[19],"we":[20],"investigate":[21],"their":[22,40],"interaction":[23],"with":[24,50],"algorithms":[25],"for":[26],"testing":[27],"equality":[28],"unification.":[30],"We":[31],"propose":[32],"a":[33],"syntactic":[34],"criterion":[35],"on":[36],"which":[38],"avoids":[39],"expansion":[41],"many":[43],"cases":[44],"without":[45],"losing":[46],"soundess":[47],"or":[48],"completeness":[49],"respect":[51],"to":[52],"\u03b2\u03b7\u03b4-conversion.":[53]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
