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Heyting $$kappa $$-Frames Heyting $$kappa $$ -框架
3区 数学
Studia Logica Pub Date : 2023-10-07 DOI: 10.1007/s11225-023-10072-3
Hector Freytes, Giuseppe Sergioli
{"title":"Heyting $$kappa $$-Frames","authors":"Hector Freytes, Giuseppe Sergioli","doi":"10.1007/s11225-023-10072-3","DOIUrl":"https://doi.org/10.1007/s11225-023-10072-3","url":null,"abstract":"Abstract In the framework of algebras with infinitary operations, the equational theory of $$bigvee _{kappa }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mo>⋁</mml:mo> <mml:mi>κ</mml:mi> </mml:msub> </mml:math> -complete Heyting algebras or Heyting $$kappa $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>κ</mml:mi> </mml:math> -frames is studied. A Hilbert style calculus algebraizable in this class is formulated. Based on the infinitary structure of Heyting $$kappa $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>κ</mml:mi> </mml:math> -frames, an equational type completeness theorem related to the $$langle bigvee , wedge , rightarrow , 0 rangle $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:mo>⋁</mml:mo> <mml:mo>,</mml:mo> <mml:mo>∧</mml:mo> <mml:mo>,</mml:mo> <mml:mo>→</mml:mo> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> <mml:mo>⟩</mml:mo> </mml:mrow> </mml:math> -structure of frames is also obtained.","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135254004","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}
引用次数: 0
Sets with Dependent Elements: A Formalization of Castoriadis’ Notion of Magma 具有相关元素的集合:Castoriadis岩浆概念的形式化
3区 数学
Studia Logica Pub Date : 2023-09-28 DOI: 10.1007/s11225-023-10073-2
Athanassios Tzouvaras
{"title":"Sets with Dependent Elements: A Formalization of Castoriadis’ Notion of Magma","authors":"Athanassios Tzouvaras","doi":"10.1007/s11225-023-10073-2","DOIUrl":"https://doi.org/10.1007/s11225-023-10073-2","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135387429","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}
引用次数: 0
Semisimplicity and Congruence 3-Permutabilty for Quasivarieties with Equationally Definable Principal Congruences 具有等式可定义主同余的拟变的半简单性和同余3-置换
3区 数学
Studia Logica Pub Date : 2023-09-20 DOI: 10.1007/s11225-023-10070-5
Miguel Campercholi, Diego Vaggione
{"title":"Semisimplicity and Congruence 3-Permutabilty for Quasivarieties with Equationally Definable Principal Congruences","authors":"Miguel Campercholi, Diego Vaggione","doi":"10.1007/s11225-023-10070-5","DOIUrl":"https://doi.org/10.1007/s11225-023-10070-5","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136308922","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}
引用次数: 0
Boolean Connexive Logic and Content Relationship 布尔连接逻辑和内容关系
3区 数学
Studia Logica Pub Date : 2023-09-20 DOI: 10.1007/s11225-023-10058-1
Mateusz Klonowski, Luis Estrada-González
{"title":"Boolean Connexive Logic and Content Relationship","authors":"Mateusz Klonowski, Luis Estrada-González","doi":"10.1007/s11225-023-10058-1","DOIUrl":"https://doi.org/10.1007/s11225-023-10058-1","url":null,"abstract":"Abstract We present here some Boolean connexive logics (BCLs) that are intended to be connexive counterparts of selected Epstein’s content relationship logics (CRLs). The main motivation for analyzing such logics is to explain the notion of connexivity by means of the notion of content relationship. The article consists of two parts. In the first one, we focus on the syntactic analysis by means of axiomatic systems. The starting point for our syntactic considerations will be the smallest BCL and the smallest CRL. In the first part, we also identify axioms of Epstein’s logics that, together with the connexive principles, lead to contradiction. Moreover, we present some principles that will be equivalent to the connexive theses, but not to the content connexive theses we will propose. In the second part, we focus on the semantic analysis provided by relating- and set-assignment models. We define sound and complete relating semantics for all tested systems. We also indicate alternative relating models for the smallest BCL, which are not alternative models of the connexive counterparts of the considered CRLs. We provide a set-assignment semantics for some BCLs, giving thus a natural formalization of the content relationship understood either as content sharing or as content inclusion.","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136308935","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}
引用次数: 0
Unary Interpretability Logics for Sublogics of the Interpretability Logic $$textbf{IL}$$ 可解释性逻辑子逻辑的一元可解释性逻辑 $$textbf{IL}$$
3区 数学
Studia Logica Pub Date : 2023-09-20 DOI: 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":null,"pages":null},"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}
引用次数: 0
Intuitionistic Public Announcement Logic with Distributed Knowledge 基于分布式知识的直觉性公告逻辑
3区 数学
Studia Logica Pub Date : 2023-09-15 DOI: 10.1007/s11225-023-10066-1
Ryo Murai, Katsuhiko Sano
{"title":"Intuitionistic Public Announcement Logic with Distributed Knowledge","authors":"Ryo Murai, Katsuhiko Sano","doi":"10.1007/s11225-023-10066-1","DOIUrl":"https://doi.org/10.1007/s11225-023-10066-1","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135436250","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}
引用次数: 0
Decidability of Lattice Equations 格方程的可判定性
3区 数学
Studia Logica Pub Date : 2023-09-15 DOI: 10.1007/s11225-023-10063-4
Nikolaos Galatos
{"title":"Decidability of Lattice Equations","authors":"Nikolaos Galatos","doi":"10.1007/s11225-023-10063-4","DOIUrl":"https://doi.org/10.1007/s11225-023-10063-4","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135437150","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}
引用次数: 0
Intuitionistic Modal Algebras 直觉模态代数
3区 数学
Studia Logica Pub Date : 2023-09-15 DOI: 10.1007/s11225-023-10065-2
Sergio A. Celani, Umberto Rivieccio
{"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":null,"pages":null},"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}
引用次数: 0
Correspondence Theory for Modal Fairtlough–Mendler Semantics of Intuitionistic Modal Logic 直觉模态逻辑中模态fairfull - mendler语义的对应理论
3区 数学
Studia Logica Pub Date : 2023-08-29 DOI: 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":null,"pages":null},"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}
引用次数: 0
Systems for Non-Reflexive Consequence 非自反性结果系统
IF 0.7 3区 数学
Studia Logica Pub Date : 2023-08-10 DOI: 10.1007/s11225-023-10049-2
Carlo Nicolai, Lorenzo Rossi
{"title":"Systems for Non-Reflexive Consequence","authors":"Carlo Nicolai, Lorenzo Rossi","doi":"10.1007/s11225-023-10049-2","DOIUrl":"https://doi.org/10.1007/s11225-023-10049-2","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76258434","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}
引用次数: 0
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