{"id":"https://openalex.org/W1675153725","doi":"https://doi.org/10.1007/3-540-58085-9_84","title":"Type theory and the informal language of mathematics","display_name":"Type theory and the informal language of mathematics","publication_year":1994,"publication_date":"1994-01-01","ids":{"openalex":"https://openalex.org/W1675153725","doi":"https://doi.org/10.1007/3-540-58085-9_84","mag":"1675153725"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-58085-9_84","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-58085-9_84","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/A5054491296","display_name":"Aarne Ranta","orcid":"https://orcid.org/0000-0002-5060-1598"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Aarne Ranta","raw_affiliation_strings":["Department of Philosophy, University of Helsinki, P.O.Box 24, 00014, Finland","#N##TAB##TAB##TAB##TAB# University of Helsinki#N##TAB##TAB##TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Philosophy, University of Helsinki, P.O.Box 24, 00014, Finland","institution_ids":["https://openalex.org/I133731052"]},{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# University of Helsinki#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I133731052"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054491296"],"corresponding_institution_ids":["https://openalex.org/I133731052"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.4213,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.79908791,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"352","last_page":"365"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9983000159263611,"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":0.9983000159263611,"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":0.9790999889373779,"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/T11567","display_name":"semigroups and automata theory","score":0.9760000109672546,"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/generative-grammar","display_name":"Generative grammar","score":0.6877356767654419},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6332802772521973},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.582856297492981},{"id":"https://openalex.org/keywords/grammar","display_name":"Grammar","score":0.5784609317779541},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.5481099486351013},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.5440787672996521},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.534213662147522},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.522250235080719},{"id":"https://openalex.org/keywords/formal-system","display_name":"Formal system","score":0.4457295536994934},{"id":"https://openalex.org/keywords/emergent-grammar","display_name":"Emergent grammar","score":0.4285227656364441},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36260300874710083},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.3336414694786072},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28818726539611816},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2586010694503784},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.21953797340393066}],"concepts":[{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.6877356767654419},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6332802772521973},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.582856297492981},{"id":"https://openalex.org/C26022165","wikidata":"https://www.wikidata.org/wiki/Q8091","display_name":"Grammar","level":2,"score":0.5784609317779541},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.5481099486351013},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.5440787672996521},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.534213662147522},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.522250235080719},{"id":"https://openalex.org/C102315432","wikidata":"https://www.wikidata.org/wiki/Q649732","display_name":"Formal system","level":2,"score":0.4457295536994934},{"id":"https://openalex.org/C69298649","wikidata":"https://www.wikidata.org/wiki/Q6045214","display_name":"Emergent grammar","level":3,"score":0.4285227656364441},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36260300874710083},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3336414694786072},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28818726539611816},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2586010694503784},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.21953797340393066},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/3-540-58085-9_84","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-58085-9_84","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.6.5189","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.5189","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.chalmers.se/~aarne/./doc/../articles/nijmegen.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.8299999833106995}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W14213647","https://openalex.org/W341008945","https://openalex.org/W569543113","https://openalex.org/W603196623","https://openalex.org/W1511133369","https://openalex.org/W1565235297","https://openalex.org/W1734944212","https://openalex.org/W1992022411","https://openalex.org/W2067558609","https://openalex.org/W2078334802","https://openalex.org/W2125151981","https://openalex.org/W4229781645"],"related_works":["https://openalex.org/W2391971764","https://openalex.org/W2386000789","https://openalex.org/W2360874615","https://openalex.org/W2382402377","https://openalex.org/W2374712251","https://openalex.org/W2380075625","https://openalex.org/W2381236562","https://openalex.org/W3137171911","https://openalex.org/W2356533048","https://openalex.org/W2383604876"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}