{"id":"https://openalex.org/W1964089759","doi":"https://doi.org/10.1080/11663081.1999.10510971","title":"Hyperboolean Algebras and Hyperboolean Modal Logic","display_name":"Hyperboolean Algebras and Hyperboolean Modal Logic","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W1964089759","doi":"https://doi.org/10.1080/11663081.1999.10510971","mag":"1964089759"},"language":"en","primary_location":{"id":"doi:10.1080/11663081.1999.10510971","is_oa":true,"landing_page_url":"https://doi.org/10.1080/11663081.1999.10510971","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/11663081.1999.10510971","source":{"id":"https://openalex.org/S93822064","display_name":"Journal of Applied Non-Classical Logics","issn_l":"1166-3081","issn":["1166-3081","1958-5780"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Non-Classical Logics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.tandfonline.com/doi/abs/10.1080/11663081.1999.10510971","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066665696","display_name":"Valentin Goranko","orcid":"https://orcid.org/0000-0002-0157-1644"},"institutions":[{"id":"https://openalex.org/I24027795","display_name":"University of Johannesburg","ror":"https://ror.org/04z6c2n17","country_code":"ZA","type":"education","lineage":["https://openalex.org/I24027795"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Valentin Goranko","raw_affiliation_strings":["Department of Mathematics, Rand Afrikaans University, PO box 524, Auckland Park, 2006, Johannesburg, South Africa E-mail: vfg@na.rau.ac.za","Department of Mathematics , Rand Afrikaans University , PO box 524, Auckland Park, 2006 , Johannesburg , South Africa E-mail: vfg@na.rau.ac.za"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Rand Afrikaans University, PO box 524, Auckland Park, 2006, Johannesburg, South Africa E-mail: vfg@na.rau.ac.za","institution_ids":["https://openalex.org/I24027795"]},{"raw_affiliation_string":"Department of Mathematics , Rand Afrikaans University , PO box 524, Auckland Park, 2006 , Johannesburg , South Africa E-mail: vfg@na.rau.ac.za","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076246494","display_name":"Dimiter Vakarelov","orcid":null},"institutions":[{"id":"https://openalex.org/I58918642","display_name":"Sofia University \"St. Kliment Ohridski\"","ror":"https://ror.org/02jv3k292","country_code":"BG","type":"education","lineage":["https://openalex.org/I58918642"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Dimiter Vakarelov","raw_affiliation_strings":["Department of Mathematical Logic with Laboratory for Applied Logic, Faculty of Mathematics and Computer Science, Sofia University, bd James Bouchier 5, 1126, Sofia, Bulgaria E-mail: dvak@fmi.uni-sofia.bg","Department of Mathematical Logic with Laboratory for Applied Logic, Faculty of Mathematics and Computer Science , Sofia University , bd James Bouchier 5, 1126 , Sofia , Bulgaria E-mail: dvak@fmi.uni-sofia.bg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Logic with Laboratory for Applied Logic, Faculty of Mathematics and Computer Science, Sofia University, bd James Bouchier 5, 1126, Sofia, Bulgaria E-mail: dvak@fmi.uni-sofia.bg","institution_ids":["https://openalex.org/I58918642"]},{"raw_affiliation_string":"Department of Mathematical Logic with Laboratory for Applied Logic, Faculty of Mathematics and Computer Science , Sofia University , bd James Bouchier 5, 1126 , Sofia , Bulgaria E-mail: dvak@fmi.uni-sofia.bg","institution_ids":["https://openalex.org/I58918642"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5399,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.75361734,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"9","issue":"2-3","first_page":"345","last_page":"368"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9994000196456909,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.979200005531311,"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/algebraic-semantics","display_name":"Algebraic semantics","score":0.7905600070953369},{"id":"https://openalex.org/keywords/interior-algebra","display_name":"Interior algebra","score":0.7204902172088623},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.6819371581077576},{"id":"https://openalex.org/keywords/modal-operator","display_name":"Modal operator","score":0.6729121208190918},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5996074080467224},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.5704932808876038},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.5467882752418518},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5261525511741638},{"id":"https://openalex.org/keywords/kripke-semantics","display_name":"Kripke semantics","score":0.5131922364234924},{"id":"https://openalex.org/keywords/s5","display_name":"S5","score":0.4921347498893738},{"id":"https://openalex.org/keywords/accessibility-relation","display_name":"Accessibility relation","score":0.48136574029922485},{"id":"https://openalex.org/keywords/modal-\u03bc-calculus","display_name":"Modal \u03bc-calculus","score":0.4813407361507416},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.4644259214401245},{"id":"https://openalex.org/keywords/stones-representation-theorem-for-boolean-algebras","display_name":"Stone's representation theorem for Boolean algebras","score":0.46065235137939453},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.44258028268814087},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3451753258705139},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.3196471333503723},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2549422085285187},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.22158849239349365},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.13409742712974548},{"id":"https://openalex.org/keywords/non-associative-algebra","display_name":"Non-associative algebra","score":0.10526809096336365},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.10282507538795471}],"concepts":[{"id":"https://openalex.org/C2779729104","wikidata":"https://www.wikidata.org/wiki/Q4724013","display_name":"Algebraic semantics","level":3,"score":0.7905600070953369},{"id":"https://openalex.org/C203254541","wikidata":"https://www.wikidata.org/wiki/Q10894825","display_name":"Interior algebra","level":5,"score":0.7204902172088623},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.6819371581077576},{"id":"https://openalex.org/C78344899","wikidata":"https://www.wikidata.org/wiki/Q638442","display_name":"Modal operator","level":4,"score":0.6729121208190918},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5996074080467224},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.5704932808876038},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.5467882752418518},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5261525511741638},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.5131922364234924},{"id":"https://openalex.org/C192609573","wikidata":"https://www.wikidata.org/wiki/Q7388341","display_name":"S5","level":5,"score":0.4921347498893738},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.48136574029922485},{"id":"https://openalex.org/C173125200","wikidata":"https://www.wikidata.org/wiki/Q5275729","display_name":"Modal \u03bc-calculus","level":5,"score":0.4813407361507416},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.4644259214401245},{"id":"https://openalex.org/C10021369","wikidata":"https://www.wikidata.org/wiki/Q1166774","display_name":"Stone's representation theorem for Boolean algebras","level":5,"score":0.46065235137939453},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.44258028268814087},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3451753258705139},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3196471333503723},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2549422085285187},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.22158849239349365},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.13409742712974548},{"id":"https://openalex.org/C518143113","wikidata":"https://www.wikidata.org/wiki/Q4391941","display_name":"Non-associative algebra","level":4,"score":0.10526809096336365},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.10282507538795471},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1080/11663081.1999.10510971","is_oa":true,"landing_page_url":"https://doi.org/10.1080/11663081.1999.10510971","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/11663081.1999.10510971","source":{"id":"https://openalex.org/S93822064","display_name":"Journal of Applied Non-Classical Logics","issn_l":"1166-3081","issn":["1166-3081","1958-5780"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Non-Classical Logics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.37.4047","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.4047","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://general.rau.ac.za/maths/goranko/papers/hbml.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.39.4159","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.4159","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.irit.fr/ACTIVITES/EQ_ALG/Gasquet/Pub/val.ps","raw_type":"text"},{"id":"pmh:oai:philarchive.org/rec/GORHAA-2","is_oa":false,"landing_page_url":"https://philarchive.org/rec/GORHAA-2","pdf_url":null,"source":{"id":"https://openalex.org/S4306402130","display_name":"PhilPapers (PhilPapers Foundation)","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:philpapers.org/rec/GORHAA-2","is_oa":false,"landing_page_url":"https://philpapers.org/rec/GORHAA-2","pdf_url":null,"source":{"id":"https://openalex.org/S4306402130","display_name":"PhilPapers (PhilPapers Foundation)","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1080/11663081.1999.10510971","is_oa":true,"landing_page_url":"https://doi.org/10.1080/11663081.1999.10510971","pdf_url":"https://www.tandfonline.com/doi/abs/10.1080/11663081.1999.10510971","source":{"id":"https://openalex.org/S93822064","display_name":"Journal of Applied Non-Classical Logics","issn_l":"1166-3081","issn":["1166-3081","1958-5780"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Non-Classical Logics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1964089759.pdf","grobid_xml":"https://content.openalex.org/works/W1964089759.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W65541081","https://openalex.org/W102788636","https://openalex.org/W1531702563","https://openalex.org/W1534873969","https://openalex.org/W1603602114","https://openalex.org/W1981936535","https://openalex.org/W1991748341","https://openalex.org/W1992205482","https://openalex.org/W2011132281","https://openalex.org/W2023648368","https://openalex.org/W2042622894","https://openalex.org/W2061003582","https://openalex.org/W2064773636","https://openalex.org/W2074899782","https://openalex.org/W2077969106","https://openalex.org/W2084752015","https://openalex.org/W2093270475","https://openalex.org/W2153417525","https://openalex.org/W2280207958","https://openalex.org/W2315064349","https://openalex.org/W4212906250","https://openalex.org/W4240175364","https://openalex.org/W4285719527","https://openalex.org/W4293176479"],"related_works":["https://openalex.org/W4233254255","https://openalex.org/W4246138424","https://openalex.org/W2534562289","https://openalex.org/W2352549085","https://openalex.org/W75246058","https://openalex.org/W2955527730","https://openalex.org/W2123071520","https://openalex.org/W2795425183","https://openalex.org/W2604713618","https://openalex.org/W3098602556"],"abstract_inverted_index":{"Hyperboolean":[0],"algebras":[1,4,9,49],"are":[2,45],"Boolean":[3,16,48,56],"with":[5,33],"operators,":[6],"constructed":[7],"as":[8],"of":[10,15,47,68,81,99,108],"complexes":[11],"(or,":[12],"power":[13],"structures)":[14],"algebras.":[17],"They":[18],"provide":[19],"an":[20],"algebraic":[21],"semantics":[22,36],"for":[23,113],"a":[24,29,34,65,88,106],"modal":[25,31,62],"logic":[26],"(called":[27],"here":[28],"hyperboolean":[30,61,94],"logic)":[32],"Kripke":[35],"accordingly":[37],"based":[38],"on":[39],"frames":[40],"in":[41,93],"which":[42],"the":[43,51,55,60,75,85],"worlds":[44],"elements":[46],"and":[50,70,96,111],"relations":[52],"correspond":[53],"to":[54],"operations.":[57],"We":[58],"introduce":[59],"logic,":[63],"give":[64],"complete":[66],"axiomatization":[67,82],"it,":[69],"show":[71],"that":[72,87],"it":[73],"lacks":[74],"finite":[76],"model":[77],"property.":[78],"The":[79],"method":[80],"hinges":[83],"upon":[84],"fact":[86],"\u201cdifference\u201d":[89],"operator":[90],"is":[91],"definable":[92],"algebras,":[95],"makes":[97],"use":[98],"additional":[100],"non-Hilbert-style":[101],"rules.":[102],"Finally,":[103],"we":[104],"discuss":[105],"number":[107],"open":[109],"questions":[110],"directions":[112],"further":[114],"research.":[115]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
