{"id":"https://openalex.org/W2139985033","doi":"https://doi.org/10.1002/malq.200310132","title":"Categorical abstract algebraic logic: Gentzen\u03c0 -institutions and the deduction-detachment property","display_name":"Categorical abstract algebraic logic: Gentzen\u03c0 -institutions and the deduction-detachment property","publication_year":2005,"publication_date":"2005-09-29","ids":{"openalex":"https://openalex.org/W2139985033","doi":"https://doi.org/10.1002/malq.200310132","mag":"2139985033"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200310132","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200310132","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"MLQ","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/A5078947872","display_name":"George Voutsadakis","orcid":"https://orcid.org/0000-0002-6854-6232"},"institutions":[{"id":"https://openalex.org/I147276918","display_name":"Lake Superior State University","ror":"https://ror.org/00yeysh84","country_code":"US","type":"education","lineage":["https://openalex.org/I147276918"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"George Voutsadakis","raw_affiliation_strings":["School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, MI 49783, USA","School of Mathematics and Computer Science Lake Superior State University Sault Sainte Marie, MI 49783, USA"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, MI 49783, USA","institution_ids":["https://openalex.org/I147276918"]},{"raw_affiliation_string":"School of Mathematics and Computer Science Lake Superior State University Sault Sainte Marie, MI 49783, USA","institution_ids":["https://openalex.org/I147276918"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078947872"],"corresponding_institution_ids":["https://openalex.org/I147276918"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.7027,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.72521076,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"51","issue":"6","first_page":"570","last_page":"578"},"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":0.9923999905586243,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9803000092506409,"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/mathematics","display_name":"Mathematics","score":0.7419757843017578},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6767311096191406},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6460422873497009},{"id":"https://openalex.org/keywords/analogy","display_name":"Analogy","score":0.6282726526260376},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.6115348935127258},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.532148540019989},{"id":"https://openalex.org/keywords/institution","display_name":"Institution","score":0.5099862813949585},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.48730361461639404},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4673742651939392},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4297051429748535},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3511433005332947},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.13174954056739807},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.09690514206886292},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07166269421577454},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.06857743859291077}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7419757843017578},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6767311096191406},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6460422873497009},{"id":"https://openalex.org/C521332185","wikidata":"https://www.wikidata.org/wiki/Q185816","display_name":"Analogy","level":2,"score":0.6282726526260376},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.6115348935127258},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.532148540019989},{"id":"https://openalex.org/C2780510313","wikidata":"https://www.wikidata.org/wiki/Q178706","display_name":"Institution","level":2,"score":0.5099862813949585},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.48730361461639404},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4673742651939392},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4297051429748535},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3511433005332947},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.13174954056739807},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.09690514206886292},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07166269421577454},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.06857743859291077},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.200310132","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200310132","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"MLQ","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W89386314","https://openalex.org/W98985150","https://openalex.org/W372357271","https://openalex.org/W605364582","https://openalex.org/W1506976087","https://openalex.org/W1518264298","https://openalex.org/W1519453649","https://openalex.org/W1540355970","https://openalex.org/W1554619471","https://openalex.org/W1560156849","https://openalex.org/W1576273408","https://openalex.org/W1579373647","https://openalex.org/W1582926964","https://openalex.org/W1847493312","https://openalex.org/W1967899636","https://openalex.org/W2010883554","https://openalex.org/W2021257181","https://openalex.org/W2035905236","https://openalex.org/W2036183559","https://openalex.org/W2049140460","https://openalex.org/W2053085623","https://openalex.org/W2069832399","https://openalex.org/W2071265130","https://openalex.org/W2077395144","https://openalex.org/W2085660860","https://openalex.org/W2203070491","https://openalex.org/W2253467077","https://openalex.org/W2493333586","https://openalex.org/W2599657867","https://openalex.org/W2914821813","https://openalex.org/W2947556356","https://openalex.org/W2973533397","https://openalex.org/W6603644293"],"related_works":["https://openalex.org/W2392206215","https://openalex.org/W2365201483","https://openalex.org/W2355561779","https://openalex.org/W2352407775","https://openalex.org/W2186567693","https://openalex.org/W108701362","https://openalex.org/W2469799552","https://openalex.org/W2768582344","https://openalex.org/W2615704157","https://openalex.org/W28964973"],"abstract_inverted_index":{"Given":[0],"a":[1,6,36,41,46,51,56,103],"\u03c0":[2,9,38,43,47],"-institution":[3,39,48],"I":[4,11,22,30,66,69,76,89],",":[5,93],"hierarchy":[7],"of":[8,29,35,68,75,82],"-institutions":[10],"(n":[12,23],")":[13,24],"is":[14,40,70,86,90,96],"constructed,":[15],"for":[16],"n":[17],"\u2265":[18],"1.":[19],"We":[20],"call":[21],"the":[25,62,73,79,83,113],"n-th":[26],"order":[27,64],"counterpart":[28,34,65],".":[31,77,116],"The":[32],"second-order":[33],"deductive":[37,105],"Gentzen":[42,53,92],"-institution,":[44],"i.e.":[45,94],"associated":[49],"with":[50],"structural":[52],"system":[54],"in":[55],"canonical":[57],"way.":[58],"So,":[59],"by":[60],"analogy,":[61],"second":[63],"(2)":[67],"also":[71],"called":[72],"\u201cGentzenization\u201d":[74],"In":[78],"main":[80],"result":[81],"paper,":[84],"it":[85,95,111],"shown":[87],"that":[88],"strongly":[91],"deductively":[97],"equivalent":[98],"to":[99],"its":[100],"Gentzenization":[101],"via":[102],"special":[104],"equivalence,":[106],"if":[107,110],"and":[108],"only":[109],"has":[112],"deduction-detachment":[114],"property":[115],"(\u00a9":[117],"2005":[118],"WILEY-VCH":[119],"Verlag":[120],"GmbH":[121],"&":[122],"Co.":[123],"KGaA,":[124],"Weinheim)":[125]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}