{"id":"https://openalex.org/W2064216040","doi":"https://doi.org/10.1109/tpami.1981.4767050","title":"Deduction Plans: A Basis for Intelligent Backtracking","display_name":"Deduction Plans: A Basis for Intelligent Backtracking","publication_year":1981,"publication_date":"1981-01-01","ids":{"openalex":"https://openalex.org/W2064216040","doi":"https://doi.org/10.1109/tpami.1981.4767050","mag":"2064216040","pmid":"https://pubmed.ncbi.nlm.nih.gov/21868918"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.1981.4767050","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1981.4767050","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5114258781","display_name":"Philip T. Cox","orcid":null},"institutions":[{"id":"https://openalex.org/I39854758","display_name":"Auckland University of Technology","ror":"https://ror.org/01zvqw119","country_code":"NZ","type":"education","lineage":["https://openalex.org/I39854758"]},{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA","NZ"],"is_corresponding":true,"raw_author_name":"Philip T. Cox","raw_affiliation_strings":["Department of Computer Science, University of Waterloo, Waterloo, Ont., Canada; Department of Computer Science, Auckland University, Auckland, Australia","Department of Computer Science, Auckland University of Technology, Auckland, New Zealand","Department of Computer Science, University of Waterloo, Waterloo, ONT, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Waterloo, Waterloo, Ont., Canada; Department of Computer Science, Auckland University, Auckland, Australia","institution_ids":[]},{"raw_affiliation_string":"Department of Computer Science, Auckland University of Technology, Auckland, New Zealand","institution_ids":["https://openalex.org/I39854758"]},{"raw_affiliation_string":"Department of Computer Science, University of Waterloo, Waterloo, ONT, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091299355","display_name":"Tomasz Pietrzykowski","orcid":"https://orcid.org/0000-0003-0428-7021"},"institutions":[{"id":"https://openalex.org/I92688161","display_name":"Acadia University","ror":"https://ror.org/00839we02","country_code":"CA","type":"education","lineage":["https://openalex.org/I92688161"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Tomasz Pietrzykowski","raw_affiliation_strings":["School of Computer Science, Acadia University, Wolfville, NS, Canada"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, Acadia University, Wolfville, NS, Canada","institution_ids":["https://openalex.org/I92688161"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5114258781"],"corresponding_institution_ids":["https://openalex.org/I151746483","https://openalex.org/I39854758"],"apc_list":null,"apc_paid":null,"fwci":7.3614,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.96447238,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"PAMI-3","issue":"1","first_page":"52","last_page":"65"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9991000294685364,"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"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9951000213623047,"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/backtracking","display_name":"Backtracking","score":0.9303185939788818},{"id":"https://openalex.org/keywords/unification","display_name":"Unification","score":0.726766049861908},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.652010977268219},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5918745994567871},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5801543593406677},{"id":"https://openalex.org/keywords/substitution","display_name":"Substitution (logic)","score":0.5781192779541016},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5051296353340149},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4859501123428345},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.4527105391025543},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42302757501602173},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38552579283714294},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35272789001464844}],"concepts":[{"id":"https://openalex.org/C156884757","wikidata":"https://www.wikidata.org/wiki/Q798554","display_name":"Backtracking","level":2,"score":0.9303185939788818},{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.726766049861908},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.652010977268219},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5918745994567871},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5801543593406677},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.5781192779541016},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5051296353340149},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4859501123428345},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.4527105391025543},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42302757501602173},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38552579283714294},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35272789001464844},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.1981.4767050","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1981.4767050","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:21868918","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21868918","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1514729613","https://openalex.org/W1530765221","https://openalex.org/W1546616265","https://openalex.org/W1606866873","https://openalex.org/W1764055246","https://openalex.org/W1963804765","https://openalex.org/W1970045008","https://openalex.org/W2000750196","https://openalex.org/W2005090804","https://openalex.org/W2021473914","https://openalex.org/W2064216040","https://openalex.org/W2100738443","https://openalex.org/W2171376204","https://openalex.org/W2293235079","https://openalex.org/W2914936697","https://openalex.org/W4229861117","https://openalex.org/W4232574302","https://openalex.org/W4246345775","https://openalex.org/W4300303686"],"related_works":["https://openalex.org/W2367630557","https://openalex.org/W101666983","https://openalex.org/W2760348722","https://openalex.org/W2783885583","https://openalex.org/W2120095724","https://openalex.org/W4238057753","https://openalex.org/W13110289","https://openalex.org/W172159181","https://openalex.org/W3100311625","https://openalex.org/W2061644010"],"abstract_inverted_index":{"A":[0,141],"proof":[1],"procedure":[2],"is":[3,72,144,169],"described":[4],"that":[5,27,175,212],"relies":[6],"on":[7,37,195],"the":[8,19,38,57,73,117,183,196,202,209,215],"construction":[9,197],"of":[10,21,40,59,70,81,85,101,110,116,160,198,205,208],"certain":[11],"directed":[12],"graphs":[13],"called":[14],"``deduction":[15],"plans.''":[16],"Plans":[17],"represent":[18],"structure":[20,48],"proofs":[22],"in":[23,56,138],"such":[24,104],"a":[25,60,124,130,167,191],"way":[26],"problem":[28],"reduction":[29],"may":[30,63],"be":[31,65,127,164,172,179],"used":[32,66],"without":[33],"imposing":[34],"any":[35],"ordering":[36,109],"solution":[39],"subproblems,":[41,111],"as":[42,67,105],"required":[43],"by":[44,146,187],"other":[45],"systems.":[46,189],"The":[47,158],"also":[49],"allows":[50,123],"access":[51],"to":[52,90,126,129,150,171],"all":[53],"clauses":[54],"deduced":[55],"course":[58],"proof,":[61],"which":[62],"then":[64],"lemmas.":[68,82],"Economy":[69],"representation":[71],"maximum":[74],"attainable,":[75],"consistent":[76],"with":[77],"this":[78,86,134],"unrestricted":[79],"availability":[80],"Restricted":[83],"versions":[84],"deduction":[87,93,192],"system":[88,193],"correspond":[89],"existing":[91,139,188],"linear":[92],"procedures,":[94],"but":[95],"do":[96],"not":[97],"suffer":[98],"from":[99,214],"some":[100],"their":[102],"shortcomings,":[103],"redundant":[106],"representation,":[107],"strict":[108],"and":[112,153],"explicit":[113],"substitution.":[114],"One":[115],"rules":[118],"for":[119],"constructing":[120],"plans,":[121],"however,":[122],"subproblem":[125,168],"factored":[128],"previously":[131],"solved":[132],"one:":[133],"has":[135],"no":[136],"equivalent":[137],"system.":[140],"further":[142],"economy":[143],"obtained":[145],"making":[147],"it":[148],"unnecessary":[149],"perform":[151],"substitutions":[152],"calculate":[154],"most":[155],"general":[156],"unifiers.":[157],"source":[159],"unification":[161],"failure":[162],"can":[163,178,200],"located":[165],"when":[166],"found":[170],"unsolvable,":[173],"so":[174],"exact":[176],"backtracking":[177,185,217],"performed":[180,186],"rather":[181],"than":[182],"blind":[184],"Therefore,":[190],"based":[194],"plans":[199],"avoid":[201],"wasteful":[203],"search":[204,210],"irrelevant":[206],"areas":[207],"space":[211],"results":[213],"usual":[216],"methods.":[218]},"counts_by_year":[],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}