{"id":"https://openalex.org/W2023047125","doi":"https://doi.org/10.1007/3-540-54507-7_15","title":"Automated deduction with associative commutative operators","display_name":"Automated deduction with associative commutative operators","publication_year":1991,"publication_date":"1991-01-01","ids":{"openalex":"https://openalex.org/W2023047125","doi":"https://doi.org/10.1007/3-540-54507-7_15","mag":"2023047125"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-54507-7_15","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-54507-7_15","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":true,"oa_status":"green","oa_url":"https://inria.hal.science/inria-00074775","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110258641","display_name":"M. Rusinowitch","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. Rusinowitch","raw_affiliation_strings":["CRIN and INRIA-Lorraine, BP239, 54506, Vandoeuvre-les-Nancy Cedex, France","CRIN and INRIA-Lorraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CRIN and INRIA-Lorraine, BP239, 54506, Vandoeuvre-les-Nancy Cedex, France","institution_ids":["https://openalex.org/I4210121838","https://openalex.org/I1326498283"]},{"raw_affiliation_string":"CRIN and INRIA-Lorraine","institution_ids":["https://openalex.org/I4210121838","https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026634244","display_name":"Laurent Vigneron","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"L. Vigneron","raw_affiliation_strings":["CRIN and INRIA-Lorraine, BP239, 54506, Vandoeuvre-les-Nancy Cedex, France","CRIN and INRIA-Lorraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CRIN and INRIA-Lorraine, BP239, 54506, Vandoeuvre-les-Nancy Cedex, France","institution_ids":["https://openalex.org/I4210121838","https://openalex.org/I1326498283"]},{"raw_affiliation_string":"CRIN and INRIA-Lorraine","institution_ids":["https://openalex.org/I4210121838","https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.649,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.83910615,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"185","last_page":"199"},"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":0.9995999932289124,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9991000294685364,"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/associative-property","display_name":"Associative property","score":0.8468079566955566},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.8246454000473022},{"id":"https://openalex.org/keywords/rule-of-inference","display_name":"Rule of inference","score":0.818350076675415},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.8175134658813477},{"id":"https://openalex.org/keywords/unification","display_name":"Unification","score":0.7096571922302246},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6319543719291687},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.5166426301002502},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5094857811927795},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5032402873039246},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4730079472064972},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.46938249468803406},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4689081907272339},{"id":"https://openalex.org/keywords/congruence","display_name":"Congruence (geometry)","score":0.411375492811203},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37971121072769165},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37514251470565796},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3317122757434845},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2960813045501709},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17813217639923096},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10453620553016663}],"concepts":[{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.8468079566955566},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.8246454000473022},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.818350076675415},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.8175134658813477},{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.7096571922302246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6319543719291687},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.5166426301002502},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5094857811927795},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5032402873039246},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4730079472064972},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.46938249468803406},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4689081907272339},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.411375492811203},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37971121072769165},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37514251470565796},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3317122757434845},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2960813045501709},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17813217639923096},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10453620553016663},{"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":4,"locations":[{"id":"doi:10.1007/3-540-54507-7_15","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-54507-7_15","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:hdl:10068/43228","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/43228","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"R - Report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.49.1816","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.1816","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.loria.fr/pub/loria/protheo/ARTICLES_1995/RusinowitchV-AAECC95.ps.gz","raw_type":"text"},{"id":"pmh:oai:HAL:inria-00074775v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00074775","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"[Research Report] RR-1896, INRIA. 1993, pp.34","raw_type":"Reports"}],"best_oa_location":{"id":"pmh:oai:HAL:inria-00074775v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00074775","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"[Research Report] RR-1896, INRIA. 1993, pp.34","raw_type":"Reports"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W420198791","https://openalex.org/W642148642","https://openalex.org/W837997859","https://openalex.org/W1479669713","https://openalex.org/W1493914162","https://openalex.org/W1495940585","https://openalex.org/W1517701251","https://openalex.org/W1524190953","https://openalex.org/W1530441764","https://openalex.org/W1581435998","https://openalex.org/W1589182689","https://openalex.org/W1592895128","https://openalex.org/W1595374223","https://openalex.org/W1601584314","https://openalex.org/W1826824496","https://openalex.org/W1906155502","https://openalex.org/W1966048066","https://openalex.org/W1968386045","https://openalex.org/W1986088671","https://openalex.org/W1994958005","https://openalex.org/W2033288425","https://openalex.org/W2042924775","https://openalex.org/W2043314428","https://openalex.org/W2051518991","https://openalex.org/W2056016391","https://openalex.org/W2061769298","https://openalex.org/W2072984710","https://openalex.org/W2086747974","https://openalex.org/W2163152086","https://openalex.org/W4248547811","https://openalex.org/W6642673056"],"related_works":["https://openalex.org/W2760927084","https://openalex.org/W4231516329","https://openalex.org/W4236197624","https://openalex.org/W27959772","https://openalex.org/W164147662","https://openalex.org/W2170954486","https://openalex.org/W2033813295","https://openalex.org/W2592005786","https://openalex.org/W2361370539","https://openalex.org/W1499822848"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}