{"id":"https://openalex.org/W1985861536","doi":"https://doi.org/10.1093/jigpal/jzi030","title":"Multi-valued Calculi for Logics Based on Non-determinism","display_name":"Multi-valued Calculi for Logics Based on Non-determinism","publication_year":2005,"publication_date":"2005-06-24","ids":{"openalex":"https://openalex.org/W1985861536","doi":"https://doi.org/10.1093/jigpal/jzi030","mag":"1985861536"},"language":"en","primary_location":{"id":"doi:10.1093/jigpal/jzi030","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzi030","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","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/A5071426595","display_name":"Arnon Avron","orcid":"https://orcid.org/0000-0001-6831-3343"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Arnon Avron","raw_affiliation_strings":["Tel-Aviv  University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tel-Aviv  University","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024219006","display_name":"Beata Konikowska","orcid":"https://orcid.org/0000-0001-8188-8344"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Beata Konikowska","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":2.5482,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.89287249,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"13","issue":"4","first_page":"365","last_page":"387"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9994000196456909,"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":0.996999979019165,"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/semantics","display_name":"Semantics (computer science)","score":0.5606856346130371},{"id":"https://openalex.org/keywords/t-norm-fuzzy-logics","display_name":"T-norm fuzzy logics","score":0.5547604560852051},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5106802582740784},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4705534279346466},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4512481093406677},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41481876373291016},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40912166237831116},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37782716751098633},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37476009130477905},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22599664330482483},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.16294816136360168},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12974128127098083}],"concepts":[{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.5606856346130371},{"id":"https://openalex.org/C86602344","wikidata":"https://www.wikidata.org/wiki/Q7667918","display_name":"T-norm fuzzy logics","level":5,"score":0.5547604560852051},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5106802582740784},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4705534279346466},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4512481093406677},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41481876373291016},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40912166237831116},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37782716751098633},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37476009130477905},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22599664330482483},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.16294816136360168},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12974128127098083},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.0},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.0},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1093/jigpal/jzi030","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzi030","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.78.8278","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.78.8278","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tau.ac.il/~aa/articles/proof-nmatrices.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322248","display_name":"Israel Academy of Sciences and Humanities","ror":"https://ror.org/03c6c9520"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1480405493","https://openalex.org/W1481398220","https://openalex.org/W1487409515","https://openalex.org/W1492288664","https://openalex.org/W1505767531","https://openalex.org/W1514220247","https://openalex.org/W1566632003","https://openalex.org/W1571738120","https://openalex.org/W1585360482","https://openalex.org/W1635116973","https://openalex.org/W1677271966","https://openalex.org/W2007325469","https://openalex.org/W2027379370","https://openalex.org/W2052771703","https://openalex.org/W2073897909","https://openalex.org/W2074025367","https://openalex.org/W2086558934","https://openalex.org/W2093713825","https://openalex.org/W2148682918","https://openalex.org/W2165124298","https://openalex.org/W2166089338","https://openalex.org/W2168151072","https://openalex.org/W2800478439"],"related_works":["https://openalex.org/W16267316","https://openalex.org/W2375573662","https://openalex.org/W2341378906","https://openalex.org/W73496598","https://openalex.org/W2122490029","https://openalex.org/W119971517","https://openalex.org/W2067534749","https://openalex.org/W1529869727","https://openalex.org/W1595640337","https://openalex.org/W2483936993"],"abstract_inverted_index":{"Non-deterministic":[0],"matrices":[1],"(Nmatrices)":[2],"are":[3,38,105],"multiple-valued":[4],"structures":[5,81],"in":[6],"which":[7,37,104],"the":[8,42,46,56,85,111,128],"value":[9],"assigned":[10],"by":[11],"a":[12,15,24,116],"valuation":[13],"to":[14,61],"complex":[16],"formula":[17],"can":[18,96],"be":[19,97],"chosen":[20],"non-deterministically":[21],"out":[22],"of":[23,28,35,71,84,88],"certain":[25],"nonempty":[26],"set":[27],"options.":[29],"We":[30,54],"consider":[31],"two":[32],"different":[33],"types":[34,87],"semantics":[36],"based":[39,78],"on":[40,79],"Nmatrices:":[41],"dynamic":[43],"one":[44,48],"and":[45,64,108],"static":[47],"(the":[49],"latter":[50],"is":[51],"new":[52,120],"here).":[53],"use":[55],"Rasiowa-Sikorski":[57],"(R-S)":[58],"decomposition":[59],"methodology":[60],"get":[62,119],"sound":[63,107],"complete":[65,109],"proof":[66],"systems":[67,95],"employing":[68],"finite":[69],"sets":[70],"mv-signed":[72],"formulas":[73],"for":[74,110,123],"all":[75],"propositional":[76],"logics":[77,126],"such":[80],"with":[82],"either":[83],"above":[86],"semantics.":[89,114],"Later":[90],"we":[91,118],"demonstrate":[92],"how":[93],"these":[94],"converted":[98],"into":[99],"cut-free":[100],"ordinary":[101],"Gentzen":[102],"calculi":[103],"also":[106],"corresponding":[112],"non-deterministic":[113],"As":[115],"by-product,":[117],"semantic":[121],"characterizations":[122],"some":[124],"well-known":[125],"(like":[127],"logic":[129],"CAR":[130],"from":[131],"[18,":[132],"28]).":[133]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-25T15:57:00.446498","created_date":"2025-10-10T00:00:00"}