{"id":"https://openalex.org/W2206489755","doi":"https://doi.org/10.1007/s11225-015-9630-3","title":"Free and Projective Bimodal Symmetric G\u00f6del Algebras","display_name":"Free and Projective Bimodal Symmetric G\u00f6del Algebras","publication_year":2015,"publication_date":"2015-09-23","ids":{"openalex":"https://openalex.org/W2206489755","doi":"https://doi.org/10.1007/s11225-015-9630-3","mag":"2206489755"},"language":"en","primary_location":{"id":"doi:10.1007/s11225-015-9630-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11225-015-9630-3","pdf_url":null,"source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studia Logica","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/A5032651196","display_name":"Revaz Grigolia","orcid":null},"institutions":[{"id":"https://openalex.org/I102808428","display_name":"Tbilisi State University","ror":"https://ror.org/05fd1hd85","country_code":"GE","type":"education","lineage":["https://openalex.org/I102808428"]}],"countries":["GE"],"is_corresponding":true,"raw_author_name":"Revaz Grigolia","raw_affiliation_strings":["Department of Mathematical Logic and Discrete Structures, I. Javakhishvili Tbilisi State University, University str., 13, 0147, Tbilisi, Georgia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Logic and Discrete Structures, I. Javakhishvili Tbilisi State University, University str., 13, 0147, Tbilisi, Georgia","institution_ids":["https://openalex.org/I102808428"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084516751","display_name":"Tatiana Kiseliova","orcid":null},"institutions":[{"id":"https://openalex.org/I102808428","display_name":"Tbilisi State University","ror":"https://ror.org/05fd1hd85","country_code":"GE","type":"education","lineage":["https://openalex.org/I102808428"]}],"countries":["GE"],"is_corresponding":false,"raw_author_name":"Tatiana Kiseliova","raw_affiliation_strings":["Department of Mathematical Logic and Discrete Structures, I. Javakhishvili Tbilisi State University, University str., 13, 0147, Tbilisi, Georgia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Logic and Discrete Structures, I. Javakhishvili Tbilisi State University, University str., 13, 0147, Tbilisi, Georgia","institution_ids":["https://openalex.org/I102808428"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073652801","display_name":"Vladimer Odisharia","orcid":null},"institutions":[{"id":"https://openalex.org/I102808428","display_name":"Tbilisi State University","ror":"https://ror.org/05fd1hd85","country_code":"GE","type":"education","lineage":["https://openalex.org/I102808428"]}],"countries":["GE"],"is_corresponding":false,"raw_author_name":"Vladimer Odisharia","raw_affiliation_strings":["Department of Mathematical Logic and Discrete Structures, I. Javakhishvili Tbilisi State University, University str., 13, 0147, Tbilisi, Georgia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Logic and Discrete Structures, I. Javakhishvili Tbilisi State University, University str., 13, 0147, Tbilisi, Georgia","institution_ids":["https://openalex.org/I102808428"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5032651196"],"corresponding_institution_ids":["https://openalex.org/I102808428"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.10881878,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"104","issue":"1","first_page":"115","last_page":"143"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","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/T11727","display_name":"Advanced Algebra and Logic","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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9987000226974487,"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":0.984499990940094,"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":0.6089017987251282},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.5703299045562744},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.5090084075927734},{"id":"https://openalex.org/keywords/many-valued-logic","display_name":"Many-valued logic","score":0.5021686553955078},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.49241650104522705},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.48095574975013733},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.456116646528244},{"id":"https://openalex.org/keywords/dynamic-logic","display_name":"Dynamic logic (digital electronics)","score":0.44229161739349365},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.42788833379745483},{"id":"https://openalex.org/keywords/modal-operator","display_name":"Modal operator","score":0.42209258675575256},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4212295413017273},{"id":"https://openalex.org/keywords/s5","display_name":"S5","score":0.41982588171958923},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3743157386779785},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37402743101119995},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.2607167363166809},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.2413351833820343},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.23915719985961914},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18113431334495544},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.15920665860176086},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1047234833240509},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08661356568336487}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6089017987251282},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.5703299045562744},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.5090084075927734},{"id":"https://openalex.org/C150889026","wikidata":"https://www.wikidata.org/wiki/Q185502","display_name":"Many-valued logic","level":3,"score":0.5021686553955078},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.49241650104522705},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.48095574975013733},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.456116646528244},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.44229161739349365},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.42788833379745483},{"id":"https://openalex.org/C78344899","wikidata":"https://www.wikidata.org/wiki/Q638442","display_name":"Modal operator","level":4,"score":0.42209258675575256},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4212295413017273},{"id":"https://openalex.org/C192609573","wikidata":"https://www.wikidata.org/wiki/Q7388341","display_name":"S5","level":5,"score":0.41982588171958923},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3743157386779785},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37402743101119995},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.2607167363166809},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.2413351833820343},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.23915719985961914},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18113431334495544},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.15920665860176086},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1047234833240509},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08661356568336487},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C172385210","wikidata":"https://www.wikidata.org/wiki/Q5339","display_name":"Transistor","level":3,"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:10.1007/s11225-015-9630-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11225-015-9630-3","pdf_url":null,"source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studia Logica","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":22,"referenced_works":["https://openalex.org/W639782591","https://openalex.org/W1553743666","https://openalex.org/W1598466974","https://openalex.org/W1994951938","https://openalex.org/W2002442167","https://openalex.org/W2007096790","https://openalex.org/W2014085418","https://openalex.org/W2026861016","https://openalex.org/W2043855341","https://openalex.org/W2049352524","https://openalex.org/W2053722013","https://openalex.org/W2059933820","https://openalex.org/W2077311448","https://openalex.org/W2085324489","https://openalex.org/W2096482476","https://openalex.org/W2321372568","https://openalex.org/W2406929445","https://openalex.org/W2743117888","https://openalex.org/W2941630641","https://openalex.org/W2970205057","https://openalex.org/W4213165878","https://openalex.org/W4245085453"],"related_works":["https://openalex.org/W2113065347","https://openalex.org/W2963628981","https://openalex.org/W1978742134","https://openalex.org/W3099361390","https://openalex.org/W2182005681","https://openalex.org/W2135389919","https://openalex.org/W2203702288","https://openalex.org/W2605728087","https://openalex.org/W4287121698","https://openalex.org/W2206489755"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}