{"id":"https://openalex.org/W3179244314","doi":"https://doi.org/10.1007/978-3-030-79876-5_10","title":"Equational Theorem Proving Modulo","display_name":"Equational Theorem Proving Modulo","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3179244314","doi":"https://doi.org/10.1007/978-3-030-79876-5_10","mag":"3179244314"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-79876-5_10","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-79876-5_10","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-79876-5_10.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-79876-5_10.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084897489","display_name":"Dohan Kim","orcid":"https://orcid.org/0000-0003-1973-615X"},"institutions":[{"id":"https://openalex.org/I16944753","display_name":"Clarkson University","ror":"https://ror.org/03rwgpn18","country_code":"US","type":"education","lineage":["https://openalex.org/I16944753"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dohan Kim","raw_affiliation_strings":["Clarkson University, Potsdam, NY, USA"],"raw_orcid":"https://orcid.org/0000-0003-1973-615X","affiliations":[{"raw_affiliation_string":"Clarkson University, Potsdam, NY, USA","institution_ids":["https://openalex.org/I16944753"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102807110","display_name":"Christopher Lynch","orcid":"https://orcid.org/0000-0003-1141-0665"},"institutions":[{"id":"https://openalex.org/I16944753","display_name":"Clarkson University","ror":"https://ror.org/03rwgpn18","country_code":"US","type":"education","lineage":["https://openalex.org/I16944753"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher Lynch","raw_affiliation_strings":["Clarkson University, Potsdam, NY, USA"],"raw_orcid":"https://orcid.org/0000-0003-1141-0665","affiliations":[{"raw_affiliation_string":"Clarkson University, Potsdam, NY, USA","institution_ids":["https://openalex.org/I16944753"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084897489"],"corresponding_institution_ids":["https://openalex.org/I16944753"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":1.0771,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.78130131,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"166","last_page":"182"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9976999759674072,"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/modulo","display_name":"Modulo","score":0.9379557967185974},{"id":"https://openalex.org/keywords/rule-of-inference","display_name":"Rule of inference","score":0.6625128984451294},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5499130487442017},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5194496512413025},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5066009759902954},{"id":"https://openalex.org/keywords/g\u00f6dels-completeness-theorem","display_name":"G\u00f6del's completeness theorem","score":0.49495452642440796},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.47812023758888245},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.46717366576194763},{"id":"https://openalex.org/keywords/equational-logic","display_name":"Equational logic","score":0.42889320850372314},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4241839349269867},{"id":"https://openalex.org/keywords/prolog","display_name":"Prolog","score":0.4177320897579193},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32859236001968384},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3219413757324219},{"id":"https://openalex.org/keywords/rewriting","display_name":"Rewriting","score":0.24083930253982544},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2402208149433136},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23539355397224426},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19715341925621033}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.9379557967185974},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.6625128984451294},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5499130487442017},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5194496512413025},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5066009759902954},{"id":"https://openalex.org/C200116569","wikidata":"https://www.wikidata.org/wiki/Q902052","display_name":"G\u00f6del's completeness theorem","level":2,"score":0.49495452642440796},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.47812023758888245},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.46717366576194763},{"id":"https://openalex.org/C154564781","wikidata":"https://www.wikidata.org/wiki/Q5384236","display_name":"Equational logic","level":3,"score":0.42889320850372314},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4241839349269867},{"id":"https://openalex.org/C81721847","wikidata":"https://www.wikidata.org/wiki/Q163468","display_name":"Prolog","level":2,"score":0.4177320897579193},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32859236001968384},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3219413757324219},{"id":"https://openalex.org/C154690210","wikidata":"https://www.wikidata.org/wiki/Q1668499","display_name":"Rewriting","level":2,"score":0.24083930253982544},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2402208149433136},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23539355397224426},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19715341925621033},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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:10.1007/978-3-030-79876-5_10","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-79876-5_10","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-79876-5_10.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-030-79876-5_10","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-79876-5_10","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-79876-5_10.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.49000000953674316,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3179244314.pdf","grobid_xml":"https://content.openalex.org/works/W3179244314.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W53862558","https://openalex.org/W837997859","https://openalex.org/W1505627668","https://openalex.org/W1507112684","https://openalex.org/W1508003017","https://openalex.org/W1510236094","https://openalex.org/W1513764941","https://openalex.org/W1515595147","https://openalex.org/W1516599971","https://openalex.org/W1583295953","https://openalex.org/W1583508425","https://openalex.org/W1589182689","https://openalex.org/W1590427085","https://openalex.org/W2037085273","https://openalex.org/W2038734800","https://openalex.org/W2041375296","https://openalex.org/W2067259733","https://openalex.org/W2100738443","https://openalex.org/W2316113835","https://openalex.org/W2494464135","https://openalex.org/W2890451556","https://openalex.org/W2914834504","https://openalex.org/W2969778797","https://openalex.org/W3021880308","https://openalex.org/W3022449549","https://openalex.org/W3184922846","https://openalex.org/W4230919050","https://openalex.org/W6636314916"],"related_works":["https://openalex.org/W1974299393","https://openalex.org/W1924552249","https://openalex.org/W4240245069","https://openalex.org/W1984727235","https://openalex.org/W161895701","https://openalex.org/W2076368962","https://openalex.org/W1499822848","https://openalex.org/W1597663530","https://openalex.org/W1985445827","https://openalex.org/W3179244314"],"abstract_inverted_index":{"Abstract":[0],"Unlike":[1],"other":[2],"methods":[3],"for":[4,50,68,96,104],"theorem":[5,14,52],"proving":[6,15,53],"modulo":[7,16,36,54],"with":[8,17,21,56],"constrained":[9,18,57,69,94,105],"clauses":[10,19,106],"[12,":[11],"13],":[12],"equational":[13,37,51],"along":[20],"its":[22],"simplification":[23],"techniques":[24],"has":[25],"not":[26,82],"been":[27],"well":[28],"studied.":[29],"We":[30,59,99],"introduce":[31],"a":[32,47,93,101],"basic":[33],"paramodulation":[34,87],"calculus":[35],"theories":[38],"E":[39,44,55,66],"satisfying":[40],"certain":[41],"properties":[42],"of":[43,92],"and":[45,111],"present":[46,100],"new":[48],"framework":[49],"clauses.":[58],"propose":[60],"an":[61],"inference":[62,74,115],"rule":[63],"called":[64],"Generalized":[65],"-Parallel":[67],"clauses,":[70],"which":[71],"makes":[72],"our":[73,114,118],"system":[75,116],"completely":[76],"basic,":[77],"meaning":[78],"that":[79,113],"we":[80],"do":[81],"need":[83],"to":[84],"allow":[85],"any":[86],"in":[88],"the":[89],"constraint":[90],"part":[91],"clause":[95],"refutational":[97],"completeness.":[98],"saturation":[102],"procedure":[103],"based":[107],"on":[108],"relative":[109],"reducibility":[110],"show":[112],"including":[117],"contraction":[119],"rules":[120],"is":[121],"refutationally":[122],"complete.":[123]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}