Pub Date : 2023-09-20DOI: 10.1007/s11225-023-10068-z
Yuya Okawa
{"title":"Unary Interpretability Logics for Sublogics of the Interpretability Logic $$textbf{IL}$$","authors":"Yuya Okawa","doi":"10.1007/s11225-023-10068-z","DOIUrl":"https://doi.org/10.1007/s11225-023-10068-z","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136308607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-15DOI: 10.1007/s11225-023-10065-2
Sergio A. Celani, Umberto Rivieccio
Abstract Recent research on algebraic models of quasi-Nelson logic has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a nucleus . Among these various algebraic structures, for which we employ the umbrella term intuitionistic modal algebras , some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of weak implicative semilattices , whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus.
{"title":"Intuitionistic Modal Algebras","authors":"Sergio A. Celani, Umberto Rivieccio","doi":"10.1007/s11225-023-10065-2","DOIUrl":"https://doi.org/10.1007/s11225-023-10065-2","url":null,"abstract":"Abstract Recent research on algebraic models of quasi-Nelson logic has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a nucleus . Among these various algebraic structures, for which we employ the umbrella term intuitionistic modal algebras , some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of weak implicative semilattices , whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus.","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135437151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-29DOI: 10.1007/s11225-023-10064-3
Zhiguang Zhao
{"title":"Correspondence Theory for Modal Fairtlough–Mendler Semantics of Intuitionistic Modal Logic","authors":"Zhiguang Zhao","doi":"10.1007/s11225-023-10064-3","DOIUrl":"https://doi.org/10.1007/s11225-023-10064-3","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136280384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-09DOI: 10.1007/s11225-023-10062-5
M. Coniglio, A. Rodrigues
{"title":"From Belnap-Dunn Four-Valued Logic to Six-Valued Logics of Evidence and Truth","authors":"M. Coniglio, A. Rodrigues","doi":"10.1007/s11225-023-10062-5","DOIUrl":"https://doi.org/10.1007/s11225-023-10062-5","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":"57 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76020560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-03DOI: 10.1007/s11225-023-10059-0
Sándor Jenei
{"title":"Correction to: Group Representation for Even and Odd Involutive Commutative Residuated Chains","authors":"Sándor Jenei","doi":"10.1007/s11225-023-10059-0","DOIUrl":"https://doi.org/10.1007/s11225-023-10059-0","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":"258 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136327654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-03DOI: 10.1007/s11225-023-10060-7
Qianli Zeng, Ming Hsiung
{"title":"The Elimination of Direct Self-reference","authors":"Qianli Zeng, Ming Hsiung","doi":"10.1007/s11225-023-10060-7","DOIUrl":"https://doi.org/10.1007/s11225-023-10060-7","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":"40 1","pages":"1037 - 1055"},"PeriodicalIF":0.7,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80054284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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