{"id":"https://openalex.org/W1986418951","doi":"https://doi.org/10.1137/0220049","title":"Equality-Test and If-Then-Else Algebras: Axiomatization and Specification","display_name":"Equality-Test and If-Then-Else Algebras: Axiomatization and Specification","publication_year":1991,"publication_date":"1991-08-01","ids":{"openalex":"https://openalex.org/W1986418951","doi":"https://doi.org/10.1137/0220049","mag":"1986418951"},"language":"en","primary_location":{"id":"doi:10.1137/0220049","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0220049","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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":"https://openalex.org/A5006929252","display_name":"Don Pigozzi","orcid":"https://orcid.org/0000-0001-9801-0490"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Don Pigozzi","raw_affiliation_strings":["Iowa State University Ames,"],"affiliations":[{"raw_affiliation_string":"Iowa State University Ames,","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006929252"],"corresponding_institution_ids":["https://openalex.org/I173911158"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.10632411,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"20","issue":"4","first_page":"766","last_page":"805"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","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/T11727","display_name":"Advanced Algebra and Logic","score":0.9983000159263611,"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/mathematics","display_name":"Mathematics","score":0.7112334966659546},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6628403663635254},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49861693382263184},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4729180932044983},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.47022128105163574},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.448625385761261},{"id":"https://openalex.org/keywords/term-algebra","display_name":"Term algebra","score":0.42203468084335327},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.41315364837646484},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36047476530075073},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.273876428604126},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.24969980120658875},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.23090654611587524},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11370640993118286}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7112334966659546},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6628403663635254},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49861693382263184},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4729180932044983},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47022128105163574},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.448625385761261},{"id":"https://openalex.org/C170517529","wikidata":"https://www.wikidata.org/wiki/Q21998744","display_name":"Term algebra","level":5,"score":0.42203468084335327},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.41315364837646484},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36047476530075073},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.273876428604126},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.24969980120658875},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.23090654611587524},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11370640993118286},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0220049","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0220049","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1503251296","https://openalex.org/W1507136479","https://openalex.org/W1512556106","https://openalex.org/W1515544966","https://openalex.org/W1535477309","https://openalex.org/W1540695267","https://openalex.org/W1575371065","https://openalex.org/W1585256267","https://openalex.org/W1601937816","https://openalex.org/W1608098058","https://openalex.org/W1761566145","https://openalex.org/W1966748830","https://openalex.org/W1969761219","https://openalex.org/W1972401918","https://openalex.org/W1992266201","https://openalex.org/W2005281679","https://openalex.org/W2005606571","https://openalex.org/W2007898361","https://openalex.org/W2030157699","https://openalex.org/W2035625685","https://openalex.org/W2041182895","https://openalex.org/W2042828015","https://openalex.org/W2049352524","https://openalex.org/W2055563322","https://openalex.org/W2077012426","https://openalex.org/W2089622083","https://openalex.org/W2115592109","https://openalex.org/W2128124354","https://openalex.org/W2134338128","https://openalex.org/W2148995721","https://openalex.org/W2157799273","https://openalex.org/W2159709550","https://openalex.org/W2220905346","https://openalex.org/W2741950310","https://openalex.org/W2944870617","https://openalex.org/W4213165878","https://openalex.org/W4231792667","https://openalex.org/W4233604412","https://openalex.org/W4239702739","https://openalex.org/W4300128858","https://openalex.org/W4400535750"],"related_works":["https://openalex.org/W2158879714","https://openalex.org/W83970069","https://openalex.org/W2068517177","https://openalex.org/W4246559176","https://openalex.org/W2152610820","https://openalex.org/W2568076520","https://openalex.org/W3105028440","https://openalex.org/W1561068498","https://openalex.org/W3168460859","https://openalex.org/W1500285590"],"abstract_inverted_index":{"An":[0,31,212],"equality-test":[1,10,36,71,133,150,248],"algebra":[2,33,37,163,184,223],"has":[3],"a":[4,97,166,188,226,240],"two-element":[5],"Boolean":[6],"sort":[7,17],"and":[8,28,53,88,129,134,140,182,202,209,265],"an":[9,35],"operation":[11],"$eq_s":[12,20],"$":[13,43,46],"for":[14,64,99,108],"each":[15],"non-Boolean":[16],"s,":[18],"where":[19],"(x,y)$":[21],"equals":[22,47],"TRUE":[23],"if":[24,49,55],"$x":[25],"=":[26,51,57],"y$":[27],"FALSE":[29],"otherwise.":[30],"if-then-else":[32,40,83,104,120,135,267],"is":[34,73,85,90,286],"with":[38,200,246,259],"the":[39,65,79,100,109,141,159,180,221,236,247,266,279,283],"operations":[41,249,268],"$[\\_,\\_,\\_]_s":[42],"adjoined:":[44],"$[b,x,y]_s":[45],"x":[48],"$b":[50,56],"\\text{TRUE}$":[52],"y":[54],"\\text{FALSE}$.":[58],"A":[59,75],"finite":[60,76,167,189,227,241],"set":[61,168,190,228,242],"of":[62,70,78,82,103,112,115,127,132,169,191,229,243],"axioms":[63],"conditional-equational":[66,101],"(i.e.,":[67,177],"quasi-equational)":[68],"theory":[69,81,102],"algebras":[72,84,116,121],"given.":[74],"axiomatization":[77],"equational":[80,110,130],"also":[86,94],"given,":[87],"it":[89],"shown":[91],"that":[92,153,216,282],"this":[93,274],"serves":[95],"as":[96,197,250,256,270],"basis":[98],"algebras.":[105],"Finite":[106],"bases":[107],"theories":[111],"several":[113],"classes":[114],"closely":[117],"related":[118],"to":[119],"were":[122],"previously":[123],"known.":[124],"The":[125,195,254],"power":[126],"conditional":[128,192,244],"specifications":[131],"data":[136,151,214],"types":[137],"are":[138,146],"investigated,":[139],"following":[142],"results,":[143],"among":[144],"others,":[145],"obtained.":[147],"(i)":[148,198],"Every":[149],"type":[152,215],"can":[154,173,217,232],"be":[155,174,218,233],"specified":[156,176,219,234],"in":[157,178,220,235],"either":[158],"initial":[160,181,222],"or":[161],"final":[162,183],"sense":[164,224,238],"by":[165,187,207,225,239,263],"universal":[170,230],"first-order":[171],"sentences":[172,231],"completely":[175],"both":[179],"senses":[185],"simultaneously)":[186],"equations.":[193],"(ii)":[194],"same":[196,237,255],"but":[199,258],"\u201cequality-test\u201d":[201],"\u201cconditional":[203,260],"equations\u201d":[204,261],"replaced,":[205],"respectively,":[206],"\u201cif-then-else\u201d":[208],"\u201cequations.\u201d":[210],"(iii)":[211,257],"arbitrary":[213],"equations":[245],"hidden":[251,272],"operations.":[252],"(iv)":[253],"replaced":[262],"\u201cequations,\u201d":[264],"adjoined":[269],"additional":[271,280],"operations;":[273],"holds":[275],"however":[276],"only":[277],"under":[278],"hypothesis":[281],"original":[284],"specification":[285],"complete.":[287]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
