{"id":"https://openalex.org/W4409047968","doi":"https://doi.org/10.1109/tkde.2025.3556367","title":"Knowledge-Centered Dual-Process Reasoning for Math Word Problems With Large Language Models","display_name":"Knowledge-Centered Dual-Process Reasoning for Math Word Problems With Large Language Models","publication_year":2025,"publication_date":"2025-04-01","ids":{"openalex":"https://openalex.org/W4409047968","doi":"https://doi.org/10.1109/tkde.2025.3556367"},"language":"en","primary_location":{"id":"doi:10.1109/tkde.2025.3556367","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2025.3556367","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Knowledge and Data Engineering","raw_type":"journal-article"},"type":"article","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":null,"display_name":"Jiayu Liu","orcid":"https://orcid.org/0000-0001-8639-3308"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiayu Liu","raw_affiliation_strings":["School of Data Science, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei, China","School of Data Science, University of Science and Technology of China, China"],"raw_orcid":"https://orcid.org/0000-0001-8639-3308","affiliations":[{"raw_affiliation_string":"School of Data Science, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"School of Data Science, University of Science and Technology of China, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085496384","display_name":"Zhenya Huang","orcid":"https://orcid.org/0000-0003-1661-0420"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenya Huang","raw_affiliation_strings":["School of Computer Science and Technology, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei, China","School of Computer Science and Technology, University of Science and Technology of China, China"],"raw_orcid":"https://orcid.org/0000-0003-1661-0420","affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"School of Computer Science and Technology, University of Science and Technology of China, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100453156","display_name":"Qi Liu","orcid":"https://orcid.org/0000-0001-6956-5550"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qi Liu","raw_affiliation_strings":["School of Data Science, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei, China","School of Data Science, University of Science and Technology of China, China"],"raw_orcid":"https://orcid.org/0000-0001-6956-5550","affiliations":[{"raw_affiliation_string":"School of Data Science, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"School of Data Science, University of Science and Technology of China, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101672534","display_name":"Zhiyuan Ma","orcid":"https://orcid.org/0009-0003-9188-7275"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiyuan Ma","raw_affiliation_strings":["School of Computer Science and Technology, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei, China","School of Computer Science and Technology, University of Science and Technology of China, China"],"raw_orcid":"https://orcid.org/0009-0003-9188-7275","affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"School of Computer Science and Technology, University of Science and Technology of China, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028518494","display_name":"ChengXiang Zhai","orcid":"https://orcid.org/0000-0002-6434-3702"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chengxiang Zhai","raw_affiliation_strings":["Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048237545","display_name":"Enhong Chen","orcid":"https://orcid.org/0000-0002-4835-4102"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Enhong Chen","raw_affiliation_strings":["School of Computer Science and Technology, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei, China","School of Computer Science and Technology, University of Science and Technology of China, China"],"raw_orcid":"https://orcid.org/0000-0002-4835-4102","affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"School of Computer Science and Technology, University of Science and Technology of China, China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.376,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.97126835,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"37","issue":"6","first_page":"3457","last_page":"3471"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11902","display_name":"Intelligent Tutoring Systems and Adaptive Learning","score":0.9513000249862671,"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/T11902","display_name":"Intelligent Tutoring Systems and Adaptive Learning","score":0.9513000249862671,"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/T10906","display_name":"AI-based Problem Solving and Planning","score":0.9117000102996826,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.9017999768257141,"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/computer-science","display_name":"Computer science","score":0.7939885854721069},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5910235643386841},{"id":"https://openalex.org/keywords/natural-language-processing","display_name":"Natural language processing","score":0.5705860257148743},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.4865519106388092},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.48570379614830017},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4803260862827301},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2842363715171814},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.1777336299419403}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7939885854721069},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5910235643386841},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.5705860257148743},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.4865519106388092},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.48570379614830017},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4803260862827301},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2842363715171814},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.1777336299419403},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tkde.2025.3556367","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2025.3556367","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Knowledge and Data Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7900000214576721,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[{"id":"https://openalex.org/G2347697912","display_name":null,"funder_award_id":"WK2150110038","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G5540768979","display_name":null,"funder_award_id":"62337001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6991849872","display_name":null,"funder_award_id":"62477044","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":83,"referenced_works":["https://openalex.org/W2072950331","https://openalex.org/W2076177169","https://openalex.org/W2108631389","https://openalex.org/W2114994015","https://openalex.org/W2155479778","https://openalex.org/W2249233388","https://openalex.org/W2475046758","https://openalex.org/W2475757000","https://openalex.org/W2561529111","https://openalex.org/W2696607001","https://openalex.org/W2757276219","https://openalex.org/W2896457183","https://openalex.org/W2962927633","https://openalex.org/W2964710271","https://openalex.org/W3006087551","https://openalex.org/W3035498813","https://openalex.org/W3084632828","https://openalex.org/W3096342154","https://openalex.org/W3101786725","https://openalex.org/W3174583470","https://openalex.org/W3175239873","https://openalex.org/W3176371077","https://openalex.org/W3194344375","https://openalex.org/W3205586399","https://openalex.org/W3215285253","https://openalex.org/W4205131770","https://openalex.org/W4226325987","https://openalex.org/W4255700721","https://openalex.org/W4287065027","https://openalex.org/W4312634749","https://openalex.org/W4320060347","https://openalex.org/W4365512576","https://openalex.org/W4382239537","https://openalex.org/W4384198612","https://openalex.org/W4385567928","https://openalex.org/W4385568260","https://openalex.org/W4385570246","https://openalex.org/W4385571129","https://openalex.org/W4385571421","https://openalex.org/W4385572162","https://openalex.org/W4385572825","https://openalex.org/W4385574345","https://openalex.org/W4385574364","https://openalex.org/W4387757693","https://openalex.org/W4388778348","https://openalex.org/W4389519118","https://openalex.org/W4389519818","https://openalex.org/W4389524089","https://openalex.org/W4390940921","https://openalex.org/W4391407054","https://openalex.org/W4392024349","https://openalex.org/W4393160302","https://openalex.org/W4394744251","https://openalex.org/W4401024948","https://openalex.org/W4402670901","https://openalex.org/W6769627184","https://openalex.org/W6777615688","https://openalex.org/W6778883912","https://openalex.org/W6791376898","https://openalex.org/W6800751262","https://openalex.org/W6803096969","https://openalex.org/W6809646742","https://openalex.org/W6810162553","https://openalex.org/W6810730852","https://openalex.org/W6838865847","https://openalex.org/W6839198299","https://openalex.org/W6846648116","https://openalex.org/W6846874006","https://openalex.org/W6846922846","https://openalex.org/W6849891405","https://openalex.org/W6849901376","https://openalex.org/W6851775633","https://openalex.org/W6852476831","https://openalex.org/W6852799390","https://openalex.org/W6853465110","https://openalex.org/W6854838534","https://openalex.org/W6855315766","https://openalex.org/W6855483941","https://openalex.org/W6860078260","https://openalex.org/W6861750095","https://openalex.org/W6867008251","https://openalex.org/W6868077254","https://openalex.org/W6869522536"],"related_works":["https://openalex.org/W2317351040","https://openalex.org/W2952466936","https://openalex.org/W1988622314","https://openalex.org/W1569283511","https://openalex.org/W2393949104","https://openalex.org/W4236344264","https://openalex.org/W3046201198","https://openalex.org/W4293061921","https://openalex.org/W3204019825","https://openalex.org/W2296205523"],"abstract_inverted_index":{"Math":[0],"word":[1],"problem":[2],"(MWP)":[3],"serves":[4],"as":[5,123],"a":[6,65,104,129,156,162],"critical":[7],"milestone":[8],"for":[9,52,238],"assessing":[10],"the":[11,49,96,116,124,143,149,169,175,192,227,248,289],"text":[12],"mining":[13],"ability":[14],"and":[15,109,127,161,172,207,231,261,274],"knowledge":[16,50,88,125,140,170,198,236,243],"mastery":[17],"level":[18],"of":[19,196,212,293],"models.":[20],"Recent":[21],"advancements":[22],"have":[23],"witnessed":[24],"large":[25],"language":[26],"models":[27],"(LLMs)":[28],"showcasing":[29],"remarkable":[30],"performance":[31],"on":[32,184],"MWP.":[33,91],"However,":[34],"current":[35],"LLMs":[36,73,122],"still":[37],"frequently":[38],"exhibit":[39],"logical":[40],"errors,":[41],"which":[42],"highlights":[43],"their":[44,138,279],"inability":[45],"to":[46,74,83,89,99,141,167,190,225,246,265],"fully":[47],"grasp":[48],"required":[51],"genuine":[53],"step-by-step":[54],"mathematical":[55,77,146,294],"reasoning.":[56,147],"To":[57],"this":[58,61],"end,":[59],"in":[60,179,199,253],"paper,":[62],"we":[63,154,201,218],"propose":[64,155,208],"novel":[66,130],"Knowledge-guided":[67],"Solver":[68],"(KNOS)":[69],"framework":[70],"that":[71,135],"empowers":[72],"simulate":[75],"human":[76,185],"reasoning,":[78],"whose":[79],"core":[80],"idea":[81],"is":[82,244],"<italic":[84,105,111,117,131,150,157,163,221,249],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[85,106,112,118,132,151,158,164,222,250],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Invoke-Verify-Inject</i>":[86],"necessary":[87],"solve":[90],"We":[92],"draw":[93],"inspiration":[94],"from":[95,234],"dual-process":[97],"theory":[98],"construct":[100],"two":[101],"cooperative":[102],"systems:":[103],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Knowledge":[107,119],"System</i>":[108,120],"an":[110,180,203,209],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Inference":[113,152],"System</i>.":[114],"Specifically,":[115],"employs":[121],"base":[126],"develops":[128],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">knowledge":[133,159,165,223,251],"invoker</i>":[134,252],"can":[136],"elicit":[137],"relevant":[139,229],"support":[142],"strict":[144,290],"step-level":[145],"In":[148,216],"System</i>,":[153],"verifier</i>":[160],"injector</i>":[166],"evaluate":[168],"rationality":[171],"further":[173],"guide":[174],"step-wise":[176,291],"symbolic":[177],"deduction":[178],"interpretable":[181],"manner":[182],"based":[183],"cognitive":[186],"mechanism,":[187],"respectively.":[188],"Moreover,":[189],"tackle":[191],"potential":[193],"scarcity":[194],"issue":[195],"mathematics-specific":[197],"LLMs,":[200],"consider":[202],"open-book":[204],"exam":[205],"scenario":[206],"improved":[210],"version":[211],"KNOS":[213,260],"called":[214],"EKNOS.":[215],"EKNOS,":[217],"meticulously":[219],"design":[220],"selectors</i>":[224],"extract":[226],"most":[228],"commonsense":[230],"math":[232],"formulas":[233],"external":[235],"sources":[237],"each":[239],"reasoning":[240,257,280],"step.":[241],"This":[242],"utilized":[245],"assist":[247],"better":[254],"stimulating":[255],"LLMs\u2019":[256],"abilities.":[258],"Both":[259],"EKNOS":[262],"are":[263],"flexible":[264],"empower":[266],"different":[267],"LLMs.":[268],"Our":[269],"experiments":[270],"with":[271],"GPT3,":[272],"ChatGPT,":[273],"GPT4":[275],"not":[276],"only":[277],"demonstrate":[278],"accuracy":[281],"improvement":[282],"but":[283],"also":[284],"show":[285],"how":[286],"they":[287],"bring":[288],"interpretability":[292],"thinking.":[295]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4}],"updated_date":"2025-12-28T23:10:05.387466","created_date":"2025-10-10T00:00:00"}
