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Stefania Centrone, Deborah Kant, Deniz Serikaya, Reflections on the Foundations of Mathematics. Univalent Foundations, Set Theory and General Thoughts, vol. 407 of Synthese Library, Springer, 2019, pp. 494+xxviii; ISBN: 978-3-030-15654-1 (Hardcover) 149.79€, ISBN: 978-3-030-15655-8 (eBook). Stefania Centrone、Deborah Kant、Deniz Serikaya，《对数学基础的思考》。Univalent Foundations, Set Theory and General Thoughts》，Synthese Library 第 407 卷，施普林格出版社，2019 年，第 494+xxviii 页；ISBN：978-3-030-15654-1 (Hardcover) 149.79 欧元，ISBN：978-3-030-15655-8 (eBook).
IF 0.7 3区 数学
Studia Logica Pub Date : 2024-04-25 DOI: 10.1007/s11225-024-10097-2
Matteo de Ceglie
{"title":"Stefania Centrone, Deborah Kant, Deniz Serikaya, Reflections on the Foundations of Mathematics. Univalent Foundations, Set Theory and General Thoughts, vol. 407 of Synthese Library, Springer, 2019, pp. 494+xxviii; ISBN: 978-3-030-15654-1 (Hardcover) 149.79€, ISBN: 978-3-030-15655-8 (eBook).","authors":"Matteo de Ceglie","doi":"10.1007/s11225-024-10097-2","DOIUrl":"https://doi.org/10.1007/s11225-024-10097-2","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140653389","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
On a First-Order Bi-Sorted Semantically Closed Language 论一阶双排序语义封闭语言
IF 0.7 3区 数学
Studia Logica Pub Date : 2024-04-25 DOI: 10.1007/s11225-024-10104-6
Fernanda Birolli Abrahão, Edelcio Gonçalves de Souza
{"title":"On a First-Order Bi-Sorted Semantically Closed Language","authors":"Fernanda Birolli Abrahão, Edelcio Gonçalves de Souza","doi":"10.1007/s11225-024-10104-6","DOIUrl":"https://doi.org/10.1007/s11225-024-10104-6","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140653985","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
Refutations and Proofs in the Paraconsistent Modal Logics: KN4 and KN4.D 旁证模态逻辑中的反驳和证明：KN4 和 KN4.D
IF 0.7 3区 数学
Studia Logica Pub Date : 2024-04-25 DOI: 10.1007/s11225-024-10102-8
Tomasz Skura
{"title":"Refutations and Proofs in the Paraconsistent Modal Logics: KN4 and KN4.D","authors":"Tomasz Skura","doi":"10.1007/s11225-024-10102-8","DOIUrl":"https://doi.org/10.1007/s11225-024-10102-8","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140657576","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
Parameterfree Comprehension Does Not Imply Full Comprehension in Second Order Peano Arithmetic 无范式理解并不意味着完全理解二阶皮亚诺算术
IF 0.7 3区 数学
Studia Logica Pub Date : 2024-04-24 DOI: 10.1007/s11225-024-10108-2
V. Kanovei, V. Lyubetsky
{"title":"Parameterfree Comprehension Does Not Imply Full Comprehension in Second Order Peano Arithmetic","authors":"V. Kanovei, V. Lyubetsky","doi":"10.1007/s11225-024-10108-2","DOIUrl":"https://doi.org/10.1007/s11225-024-10108-2","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140664794","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
Non-Reflexive Nonsense: Proof Theory of Paracomplete Weak Kleene Logic 非反身胡言乱语：准完全弱克莱因逻辑的证明理论
IF 0.7 3区 数学
Studia Logica Pub Date : 2024-03-18 DOI: 10.1007/s11225-023-10086-x
{"title":"Non-Reflexive Nonsense: Proof Theory of Paracomplete Weak Kleene Logic","authors":"","doi":"10.1007/s11225-023-10086-x","DOIUrl":"https://doi.org/10.1007/s11225-023-10086-x","url":null,"abstract":"<h3>Abstract</h3> <p>Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic ‘of nonsense’ introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic <span> <span>(textbf{K}_{textbf{3}}^{textbf{w}})</span> </span> by Stephen C. Kleene. The main features of this calculus are (i) that it is <em>non-reflexive</em>, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where <em>no variable-inclusion conditions</em> are attached; and (iii) that it is <em>hybrid</em>, insofar as it includes both left and right operational introduction as well as elimination rules.</p>","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156137","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
Finite Hilbert Systems for Weak Kleene Logics 弱克莱因逻辑的有限希尔伯特系统
IF 0.7 3区 数学
Studia Logica Pub Date : 2024-03-16 DOI: 10.1007/s11225-023-10079-w
{"title":"Finite Hilbert Systems for Weak Kleene Logics","authors":"","doi":"10.1007/s11225-023-10079-w","DOIUrl":"https://doi.org/10.1007/s11225-023-10079-w","url":null,"abstract":"<h3>Abstract</h3> <p>Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar–Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first <em>finite</em> Hilbert-style single-conclusion axiomatizations for these logics.</p>","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156160","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
Jaśkowski and the Jains 雅斯科夫斯基和耆那教徒
IF 0.7 3区 数学
Studia Logica Pub Date : 2024-03-13 DOI: 10.1007/s11225-024-10096-3
Graham Priest
{"title":"Jaśkowski and the Jains","authors":"Graham Priest","doi":"10.1007/s11225-024-10096-3","DOIUrl":"https://doi.org/10.1007/s11225-024-10096-3","url":null,"abstract":"<p>In 1948 Jaśkowski introduced the first discussive logic. The main technical idea was to take what holds to be what is true at some possible world. Some 2,000 years earlier, Jain philosophers had advocated a similar idea, in their doctrine of <i>syādvāda</i>. Of course, these philosophers had no knowledge of contemporary logical notions; but the techniques pioneered by Jaśkowski can be deployed to make the Jain ideas mathematically precise. Moreover, Jain ideas suggest a new family of many-valued discussive logics. In this paper, I will explain all these matters.</p>","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140115858","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
Kripke-Completeness and Sequent Calculus for Quasi-Boolean Modal Logic 准布尔模态逻辑的克里普克完备性和序列微积分
IF 0.7 3区 数学
Studia Logica Pub Date : 2024-03-06 DOI: 10.1007/s11225-024-10095-4
{"title":"Kripke-Completeness and Sequent Calculus for Quasi-Boolean Modal Logic","authors":"","doi":"10.1007/s11225-024-10095-4","DOIUrl":"https://doi.org/10.1007/s11225-024-10095-4","url":null,"abstract":"<h3>Abstract</h3> <p>Quasi-Boolean modal algebras are quasi-Boolean algebras with a modal operator satisfying the interaction axiom. Sequential quasi-Boolean modal logics and the relational semantics are introduced. Kripke-completeness for some quasi-Boolean modal logics is shown by the canonical model method. We show that every descriptive persistent quasi-Boolean modal logic is canonical. The finite model property of some quasi-Boolean modal logics is proved. A cut-free Gentzen sequent calculus for the minimal quasi-Boolean logic is developed and we show that it has the Craig interpolation property.</p>","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140046758","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
Variations on the Kripke Trick 克里普克伎俩的变体
IF 0.7 3区 数学
Studia Logica Pub Date : 2024-03-06 DOI: 10.1007/s11225-023-10093-y
{"title":"Variations on the Kripke Trick","authors":"","doi":"10.1007/s11225-023-10093-y","DOIUrl":"https://doi.org/10.1007/s11225-023-10093-y","url":null,"abstract":"<h3>Abstract</h3> <p>In the early 1960s, to prove undecidability of monadic fragments of sublogics of the predicate modal logic <span> <span>(textbf{QS5})</span> </span> that include the classical predicate logic <span> <span>(textbf{QCl})</span> </span>, Saul Kripke showed how a classical atomic formula with a binary predicate letter can be simulated by a monadic modal formula. We consider adaptations of Kripke’s simulation, which we call the Kripke trick, to various modal and superintuitionistic predicate logics not considered by Kripke. We also discuss settings where the Kripke trick does not work and where, as a result, decidability of monadic modal predicate logics can be obtained.</p>","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140046573","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
On Geometric Implications 几何意义
IF 0.7 3区 数学
Studia Logica Pub Date : 2024-03-06 DOI: 10.1007/s11225-023-10094-x
{"title":"On Geometric Implications","authors":"","doi":"10.1007/s11225-023-10094-x","DOIUrl":"https://doi.org/10.1007/s11225-023-10094-x","url":null,"abstract":"<h3>Abstract</h3> <p>It is a well-known fact that although the poset of open sets of a topological space is a Heyting algebra, its Heyting implication is not necessarily stable under the inverse image of continuous functions and hence is not a geometric concept. This leaves us wondering if there is any stable family of implications that can be safely called geometric. In this paper, we will first recall the abstract notion of implication as a binary modality introduced in Akbar Tabatabai (Implication via spacetime. In: Mathematics, logic, and their philosophies: essays in honour of Mohammad Ardeshir, pp 161–216, 2021). Then, we will use a weaker version of categorical fibrations to define the geometricity of a category of pairs of spaces and implications over a given category of spaces. We will identify the greatest geometric category over the subcategories of open-irreducible (closed-irreducible) maps as a generalization of the usual injective open (closed) maps. Using this identification, we will then characterize all geometric categories over a given category <span> <span>({mathcal {S}})</span> </span>, provided that <span> <span>({mathcal {S}})</span> </span> has some basic closure properties. Specially, we will show that there is no non-trivial geometric category over the full category of spaces. Finally, as the implications we identified are also interesting in their own right, we will spend some time to investigate their algebraic properties. We will first use a Yoneda-type argument to provide a representation theorem, making the implications a part of an adjunction-style pair. Then, we will use this result to provide a Kripke-style representation for any arbitrary implication.</p>","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140046803","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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