{"id":"https://openalex.org/W2119711012","doi":"https://doi.org/10.1007/11532231_3","title":"Reasoning in Extensional Type Theory with Equality","display_name":"Reasoning in Extensional Type Theory with Equality","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2119711012","doi":"https://doi.org/10.1007/11532231_3","mag":"2119711012"},"language":"en","primary_location":{"id":"doi:10.1007/11532231_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11532231_3","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5031812667","display_name":"Chad E. Brown","orcid":"https://orcid.org/0000-0003-4050-4361"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Chad E. Brown","raw_affiliation_strings":["Universit\u00e4t des Saarlandes, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t des Saarlandes, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5031812667"],"corresponding_institution_ids":["https://openalex.org/I91712215"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.21090876,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"23","last_page":"37"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9997000098228455,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9966999888420105,"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/extensional-definition","display_name":"Extensional definition","score":0.807852029800415},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6993109583854675},{"id":"https://openalex.org/keywords/sequent-calculus","display_name":"Sequent calculus","score":0.6740577816963196},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.6569523215293884},{"id":"https://openalex.org/keywords/sequent","display_name":"Sequent","score":0.5327900052070618},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.48960286378860474},{"id":"https://openalex.org/keywords/cut-elimination-theorem","display_name":"Cut-elimination theorem","score":0.48519137501716614},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4850139319896698},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4838210940361023},{"id":"https://openalex.org/keywords/gas-meter-prover","display_name":"Gas meter prover","score":0.47400912642478943},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4413924813270569},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.41815248131752014},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40536391735076904},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34984850883483887},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.331015408039093},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32361137866973877},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15033027529716492}],"concepts":[{"id":"https://openalex.org/C136137745","wikidata":"https://www.wikidata.org/wiki/Q19515659","display_name":"Extensional definition","level":3,"score":0.807852029800415},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6993109583854675},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.6740577816963196},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.6569523215293884},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.5327900052070618},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.48960286378860474},{"id":"https://openalex.org/C111404639","wikidata":"https://www.wikidata.org/wiki/Q376166","display_name":"Cut-elimination theorem","level":4,"score":0.48519137501716614},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4850139319896698},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4838210940361023},{"id":"https://openalex.org/C159718280","wikidata":"https://www.wikidata.org/wiki/Q5526353","display_name":"Gas meter prover","level":3,"score":0.47400912642478943},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4413924813270569},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.41815248131752014},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40536391735076904},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34984850883483887},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.331015408039093},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32361137866973877},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15033027529716492},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C77928131","wikidata":"https://www.wikidata.org/wiki/Q193343","display_name":"Tectonics","level":2,"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/11532231_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11532231_3","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W914834656","https://openalex.org/W1498831097","https://openalex.org/W1541199473","https://openalex.org/W1570712623","https://openalex.org/W1602187006","https://openalex.org/W1608522276","https://openalex.org/W1769049439","https://openalex.org/W1996404651","https://openalex.org/W2034155940","https://openalex.org/W2034676877","https://openalex.org/W2040723389","https://openalex.org/W2084443499","https://openalex.org/W2084797476","https://openalex.org/W2115610240","https://openalex.org/W2162564051","https://openalex.org/W2914221638","https://openalex.org/W3174395628","https://openalex.org/W4237061074","https://openalex.org/W4285719527","https://openalex.org/W4299731435"],"related_works":["https://openalex.org/W1562648369","https://openalex.org/W2584381231","https://openalex.org/W4295728898","https://openalex.org/W4289719533","https://openalex.org/W2562634993","https://openalex.org/W3090765541","https://openalex.org/W4253113110","https://openalex.org/W1147619178","https://openalex.org/W1566344352","https://openalex.org/W2160135306"],"abstract_inverted_index":null,"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"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"}