{"id":"https://openalex.org/W1976522453","doi":"https://doi.org/10.1007/s11787-007-0013-z","title":"Abstract Logics, Logic Maps, and Logic Homomorphisms","display_name":"Abstract Logics, Logic Maps, and Logic Homomorphisms","publication_year":2007,"publication_date":"2007-08-07","ids":{"openalex":"https://openalex.org/W1976522453","doi":"https://doi.org/10.1007/s11787-007-0013-z","mag":"1976522453"},"language":"en","primary_location":{"id":"doi:10.1007/s11787-007-0013-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11787-007-0013-z","pdf_url":null,"source":{"id":"https://openalex.org/S120609085","display_name":"Logica Universalis","issn_l":"1661-8297","issn":["1661-8297","1661-8300"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logica Universalis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://repositorio.ufba.br/ri/handle/ri/14354","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015019892","display_name":"Steffen Lewitzka","orcid":"https://orcid.org/0000-0003-0685-9134"},"institutions":[{"id":"https://openalex.org/I126158947","display_name":"Universidade Federal da Bahia","ror":"https://ror.org/03k3p7647","country_code":"BR","type":"education","lineage":["https://openalex.org/I126158947"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Steffen Lewitzka","raw_affiliation_strings":["Instituto de Matem\u00e1tica Departamento de Ci\u00eancia da Computa\u00e7\u00e3o Laborat\u00f3rio de Sistemas Distribu\u00eddos\u2013LaSiD, Federal University of Bahia \u2013 UFBA, Av. Ademar de Barros, CEP 40170-110, Salvador da Bahia, BA, Brazil","Federal University of Bahia \u2013 UFBA"],"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica Departamento de Ci\u00eancia da Computa\u00e7\u00e3o Laborat\u00f3rio de Sistemas Distribu\u00eddos\u2013LaSiD, Federal University of Bahia \u2013 UFBA, Av. Ademar de Barros, CEP 40170-110, Salvador da Bahia, BA, Brazil","institution_ids":["https://openalex.org/I126158947"]},{"raw_affiliation_string":"Federal University of Bahia \u2013 UFBA","institution_ids":["https://openalex.org/I126158947"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015019892"],"corresponding_institution_ids":["https://openalex.org/I126158947"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.7487,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71101746,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"1","issue":"2","first_page":"243","last_page":"276"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9998000264167786,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9998000264167786,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9866999983787537,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9715999960899353,"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":0.7244150638580322},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.5738836526870728},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.4855789542198181},{"id":"https://openalex.org/keywords/homeomorphism","display_name":"Homeomorphism (graph theory)","score":0.4593536853790283},{"id":"https://openalex.org/keywords/t-norm-fuzzy-logics","display_name":"T-norm fuzzy logics","score":0.4586072564125061},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44999492168426514},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.44135037064552307},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.432143896818161},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4217025339603424},{"id":"https://openalex.org/keywords/\u0142ukasiewicz-logic","display_name":"\u0141ukasiewicz logic","score":0.4163854718208313},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3891885280609131},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3237295150756836},{"id":"https://openalex.org/keywords/substructural-logic","display_name":"Substructural logic","score":0.27129697799682617},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.2105334997177124},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.20764431357383728},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1740778088569641},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.14765504002571106},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.13570889830589294},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12370532751083374},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08697038888931274},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.07041168212890625}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7244150638580322},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.5738836526870728},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.4855789542198181},{"id":"https://openalex.org/C10728891","wikidata":"https://www.wikidata.org/wiki/Q584521","display_name":"Homeomorphism (graph theory)","level":2,"score":0.4593536853790283},{"id":"https://openalex.org/C86602344","wikidata":"https://www.wikidata.org/wiki/Q7667918","display_name":"T-norm fuzzy logics","level":5,"score":0.4586072564125061},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44999492168426514},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.44135037064552307},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.432143896818161},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4217025339603424},{"id":"https://openalex.org/C206321295","wikidata":"https://www.wikidata.org/wiki/Q8080919","display_name":"\u0141ukasiewicz logic","level":5,"score":0.4163854718208313},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3891885280609131},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3237295150756836},{"id":"https://openalex.org/C144760519","wikidata":"https://www.wikidata.org/wiki/Q839490","display_name":"Substructural logic","level":4,"score":0.27129697799682617},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.2105334997177124},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.20764431357383728},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1740778088569641},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.14765504002571106},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.13570889830589294},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12370532751083374},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08697038888931274},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.07041168212890625}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11787-007-0013-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11787-007-0013-z","pdf_url":null,"source":{"id":"https://openalex.org/S120609085","display_name":"Logica Universalis","issn_l":"1661-8297","issn":["1661-8297","1661-8300"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logica Universalis","raw_type":"journal-article"},{"id":"pmh:oai:agregador.ibict.br.RI_UFBA:oai:192.168.11:11:ri/14354","is_oa":false,"landing_page_url":"https://www.rcaap.pt/detail.jsp?id=oai:agregador.ibict.br.RI_UFBA:oai:192.168.11:11:ri/14354","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repositorio.ufba.br:ri/14354","is_oa":true,"landing_page_url":"http://repositorio.ufba.br/ri/handle/ri/14354","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dx.doi.org/10.1007/s11787-007-0013-z","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:repositorio.ufba.br:ri/14354","is_oa":true,"landing_page_url":"http://repositorio.ufba.br/ri/handle/ri/14354","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dx.doi.org/10.1007/s11787-007-0013-z","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"score":0.4300000071525574,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W110963011","https://openalex.org/W154551041","https://openalex.org/W1583699205","https://openalex.org/W1599991857","https://openalex.org/W2055005866"],"related_works":["https://openalex.org/W193449051","https://openalex.org/W1968826078","https://openalex.org/W637989598","https://openalex.org/W2593401383","https://openalex.org/W88232665","https://openalex.org/W2061319273","https://openalex.org/W4224275486","https://openalex.org/W1967037961","https://openalex.org/W2156897951","https://openalex.org/W2060888926"],"abstract_inverted_index":{"What":[0,12],"is":[1,13,49],"a":[2,42,56,62,71,137,141,153],"logic?":[3],"Which":[4],"properties":[5],"are":[6,112],"preserved":[7],"by":[8],"maps":[9,75,113,129],"between":[10,155],"logics?":[11,20],"the":[14,32,39,52,65,87,104,134,147,156],"right":[15],"notion":[16,135,180],"for":[17,181],"equivalence":[18,165,182],"of":[19,35,41,45,55,67,73,101,107,136,149,183],"In":[21],"order":[22],"to":[23,95,163],"give":[24],"satisfactory":[25],"answers":[26],"we":[27,171,186],"generalize":[28],"and":[29,37,76,103,122,160,178],"further":[30],"develop":[31,70],"topological":[33,89,125,158],"approach":[34],"[4]":[36],"present":[38],"foundations":[40],"general":[43],"theory":[44,72],"abstract":[46,53,59,168],"logics":[47,102],"which":[48],"based":[50],"on":[51,64,86,146,167],"concept":[54,189],"theory.":[57],"Each":[58],"logic":[60,74,128,138,173],"determines":[61],"topology":[63],"set":[66],"theories.":[68],"We":[69,91,132],"show":[77],"in":[78,116,130,195],"what":[79],"way":[80],"they":[81],"induce":[82],"(continuous,":[83],"open)":[84],"functions":[85,121],"corresponding":[88],"spaces.":[90],"also":[92],"establish":[93],"connections":[94],"well-known":[96],"notions":[97],"such":[98],"as":[99,140,175],"translations":[100],"satisfaction":[105],"axiom":[106],"institutions":[108],"[5].":[109],"Logic":[110],"homomorphisms":[111],"that":[114,151],"behave":[115],"some":[117],"sense":[118],"like":[119],"continuous":[120],"preserve":[123],"more":[124],"structure":[126],"than":[127],"general.":[131],"introduce":[133],"isomorphism":[139],"(not":[142],"necessarily":[143],"bijective)":[144],"function":[145],"sets":[148],"formulas":[150],"induces":[152],"homeomorphism":[154],"respective":[157],"spaces":[159],"gives":[161],"rise":[162],"an":[164,176],"relation":[166],"logics.":[169,184],"Therefore,":[170],"propose":[172],"isomorphisms":[174],"adequate":[177],"precise":[179],"Finally,":[185],"compare":[187],"this":[188],"with":[190],"another":[191],"recent":[192],"proposal":[193],"presented":[194],"[2].":[196]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}