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Bulletin of the Section of Logic最新文献

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On combining intuitionistic and S4 modal logic 论直观逻辑与 S4 模态逻辑的结合
Bulletin of the Section of Logic Pub Date : 2024-06-05 DOI: 10.18778/0138-0680.2024.11
J. Rasga, C. Sernadas
{"title":"On combining intuitionistic and S4 modal logic","authors":"J. Rasga, C. Sernadas","doi":"10.18778/0138-0680.2024.11","DOIUrl":"https://doi.org/10.18778/0138-0680.2024.11","url":null,"abstract":"We address the problem of combining intuitionistic and S4 modal logic in a non-collapsing way inspired by the recent works in combining intuitionistic and classical logic. The combined language includes the shared constructors of both logics namely conjunction, disjunction and falsum as well as the intuitionistic implication, the classical implication and the necessity modality.We present a Gentzen calculus for the combined logic defined over a Gentzen calculus for the host S4 modal logic. The semantics is provided by Kripke structures. The calculus is proved to be sound and complete with respect to this semantics. We also show that the combined logic is a conservative extension of each component. Finally we establish that the Gentzen calculus for the combined logic enjoys cut elimination.","PeriodicalId":505659,"journal":{"name":"Bulletin of the Section of Logic","volume":"52 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141382926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Positive Complete Theories and Positive Strong Amalgamation Property 正完全理论和正强合并特性
Bulletin of the Section of Logic Pub Date : 2024-06-04 DOI: 10.18778/0138-0680.2024.10
Mohammed Belkasmi
{"title":"Positive Complete Theories and Positive Strong Amalgamation Property","authors":"Mohammed Belkasmi","doi":"10.18778/0138-0680.2024.10","DOIUrl":"https://doi.org/10.18778/0138-0680.2024.10","url":null,"abstract":"We introduce the notion of positive strong amalgamation property and we investigate some universal forms and properties of this notion.  Considering the close relationship between the amalgamation property and the notion of complete theories,  we explore the fundamental properties of positively  complete theories, and we illustrate the behaviour of this notion by bringing  some changes to the language of the theory through the groups theory.","PeriodicalId":505659,"journal":{"name":"Bulletin of the Section of Logic","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141387596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sequent systems for consequence relations of cyclic linear logics 循环线性逻辑后果关系的序列系统
Bulletin of the Section of Logic Pub Date : 2024-04-24 DOI: 10.18778/0138-0680.2024.06
Paweł Płaczek
{"title":"Sequent systems for consequence relations of cyclic linear logics","authors":"Paweł Płaczek","doi":"10.18778/0138-0680.2024.06","DOIUrl":"https://doi.org/10.18778/0138-0680.2024.06","url":null,"abstract":"Linear Logic is a versatile framework with diverse applications in computer science and mathematics. One intriguing fragment of Linear Logic is Multiplicative-Additive Linear Logic (MALL), which forms the exponential-free component of the larger framework. Modifying MALL, researchers have explored weaker logics such as Noncommutative MALL (Bilinear Logic, BL) and Cyclic MALL (CyMALL) to investigate variations in commutativity. In this paper, we focus on Cyclic Nonassociative Bilinear Logic (CyNBL), a variant that combines noncommutativity and nonassociativity. We introduce a sequent system for CyNBL, which includes an auxiliary system for incorporating nonlogical axioms. Notably, we establish the cut elimination property for CyNBL. Moreover, we establish the strong conservativeness of CyNBL over Full Nonassociative Lambek Calculus (FNL) without additive constants. The paper highlights that all proofs are constructed using syntactic methods, ensuring their constructive nature. We provide insights into constructing cut-free proofs and establishing a logical relationship between CyNBL and FNL.","PeriodicalId":505659,"journal":{"name":"Bulletin of the Section of Logic","volume":"4 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140660831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
SUP-Hesitant Fuzzy Interior Ideals in (Gamma)-Semigroups (γ)-半群中的SUP-Hesitant Fuzzy Interior Ideals
Bulletin of the Section of Logic Pub Date : 2024-04-24 DOI: 10.18778/0138-0680.2024.09
Pannawit Khamrot, T. Gaketem
{"title":"SUP-Hesitant Fuzzy Interior Ideals in (Gamma)-Semigroups","authors":"Pannawit Khamrot, T. Gaketem","doi":"10.18778/0138-0680.2024.09","DOIUrl":"https://doi.org/10.18778/0138-0680.2024.09","url":null,"abstract":"In this paper, we defined the concept (mathcal{SUP})-hesitant fuzzy interior ideals in (Gamma)-semigroups, which is generalized of hesitant fuzzy interior ideals in (Gamma)-semigroups. Moreover, we study basic properties of (mathcal{SUP})-hesitant fuzzy interior ideals in (Gamma)-semigroups. We investigate characterized properties of those.","PeriodicalId":505659,"journal":{"name":"Bulletin of the Section of Logic","volume":"1 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140664881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
About Logically Probable Sentences 关于逻辑可能句
Bulletin of the Section of Logic Pub Date : 2024-04-23 DOI: 10.18778/0138-0680.2024.04
Adam Olszewski
{"title":"About Logically Probable Sentences","authors":"Adam Olszewski","doi":"10.18778/0138-0680.2024.04","DOIUrl":"https://doi.org/10.18778/0138-0680.2024.04","url":null,"abstract":"The starting point of this paper is the empirically determined ability to reason in natural language by employing probable sentences. A sentence is understood to be logically probable if its schema, expressed as a formula in the language of classical propositional calculus, takes the logical value of truth for the majority of Boolean valuations, i.e., as a logically probable formula. Then, the formal system P is developed to encode the set of these logically probable formulas. Based on natural semantics, a strong completeness theorem for P is proved. Alternative notions of consequence for logically probable sentences are also considered.","PeriodicalId":505659,"journal":{"name":"Bulletin of the Section of Logic","volume":"29 37","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140672216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lifting Results for Finite Dimensions to the Transfinite in Systems of Varieties Using Ultraproducts 利用超积将有限维数提升到变分系统中的无穷维数的结果
Bulletin of the Section of Logic Pub Date : 2024-02-12 DOI: 10.18778/0138-0680.2024.02
Tarek Sayed Ahmed
{"title":"Lifting Results for Finite Dimensions to the Transfinite in Systems of Varieties Using Ultraproducts","authors":"Tarek Sayed Ahmed","doi":"10.18778/0138-0680.2024.02","DOIUrl":"https://doi.org/10.18778/0138-0680.2024.02","url":null,"abstract":"We redefine a system of varieties definable by a schema of equations to include finite dimensions. Then we present a technique using ultraproducts enabling one to lift results proved for every finite dimension to the transfinite. Let (bf Ord) denote the class of all ordinals. Let (langle mathbf{K}_{alpha}: alphain bf Ordrangle) be a system of varieties definable by a schema. Given any ordinal (alpha), we define an operator (mathsf{Nr}_{alpha}) that acts on (mathbf{K}_{beta}) for any (beta>alpha) giving an algebra in (mathbf{K}_{alpha}), as an abstaction of taking (alpha)-neat reducts for cylindric algebras. We show that for any positive (k), and any infinite ordinal (alpha) that (mathbf{S}mathsf{Nr}_{alpha}mathbf{K}_{alpha+k+1}) cannot be axiomatized by a finite schema over (mathbf{S}mathsf{Nr}_{alpha}mathbf{K}_{alpha+k}) given that the result is valid for all finite dimensions greater than some fixed finite ordinal. We apply our results to cylindric algebras and Halmos quasipolyadic algebras with equality. As an application to our algebraic result we obtain a strong incompleteness theorem (in the sense that validitities are not captured by finitary Hilbert style axiomatizations) for an algebraizable extension of (L_{omega,omega}).","PeriodicalId":505659,"journal":{"name":"Bulletin of the Section of Logic","volume":"1 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139782741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lifting Results for Finite Dimensions to the Transfinite in Systems of Varieties Using Ultraproducts 利用超积将有限维数提升到变分系统中的无穷维数的结果
Bulletin of the Section of Logic Pub Date : 2024-02-12 DOI: 10.18778/0138-0680.2024.02
Tarek Sayed Ahmed
{"title":"Lifting Results for Finite Dimensions to the Transfinite in Systems of Varieties Using Ultraproducts","authors":"Tarek Sayed Ahmed","doi":"10.18778/0138-0680.2024.02","DOIUrl":"https://doi.org/10.18778/0138-0680.2024.02","url":null,"abstract":"We redefine a system of varieties definable by a schema of equations to include finite dimensions. Then we present a technique using ultraproducts enabling one to lift results proved for every finite dimension to the transfinite. Let (bf Ord) denote the class of all ordinals. Let (langle mathbf{K}_{alpha}: alphain bf Ordrangle) be a system of varieties definable by a schema. Given any ordinal (alpha), we define an operator (mathsf{Nr}_{alpha}) that acts on (mathbf{K}_{beta}) for any (beta>alpha) giving an algebra in (mathbf{K}_{alpha}), as an abstaction of taking (alpha)-neat reducts for cylindric algebras. We show that for any positive (k), and any infinite ordinal (alpha) that (mathbf{S}mathsf{Nr}_{alpha}mathbf{K}_{alpha+k+1}) cannot be axiomatized by a finite schema over (mathbf{S}mathsf{Nr}_{alpha}mathbf{K}_{alpha+k}) given that the result is valid for all finite dimensions greater than some fixed finite ordinal. We apply our results to cylindric algebras and Halmos quasipolyadic algebras with equality. As an application to our algebraic result we obtain a strong incompleteness theorem (in the sense that validitities are not captured by finitary Hilbert style axiomatizations) for an algebraizable extension of (L_{omega,omega}).","PeriodicalId":505659,"journal":{"name":"Bulletin of the Section of Logic","volume":"202 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139842602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Syntactic Proof of the Decidability of First-Order Monadic Logic 一阶单子逻辑可判性的句法证明
Bulletin of the Section of Logic Pub Date : 2024-02-09 DOI: 10.18778/0138-0680.2024.03
E. Orlandelli, Matteo Tesi
{"title":"A Syntactic Proof of the Decidability of First-Order Monadic Logic","authors":"E. Orlandelli, Matteo Tesi","doi":"10.18778/0138-0680.2024.03","DOIUrl":"https://doi.org/10.18778/0138-0680.2024.03","url":null,"abstract":"Decidability of monadic first-order classical logic was established by Löwenheim in 1915. The proof made use of a semantic argument, but a purely syntactic proof has never been provided. In the present paper we introduce a syntactic proof of decidability of monadic first-order logic in innex normal form which exploits G3-style sequent calculi. In particular, we introduce a cut- and contraction-free calculus having a (complexity optimal) terminating proof-search procedure. We also show that this logic can be faithfully embedded in the modal logic T.","PeriodicalId":505659,"journal":{"name":"Bulletin of the Section of Logic","volume":" 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139789885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Syntactic Proof of the Decidability of First-Order Monadic Logic 一阶单子逻辑可判性的句法证明
Bulletin of the Section of Logic Pub Date : 2024-02-09 DOI: 10.18778/0138-0680.2024.03
E. Orlandelli, Matteo Tesi
{"title":"A Syntactic Proof of the Decidability of First-Order Monadic Logic","authors":"E. Orlandelli, Matteo Tesi","doi":"10.18778/0138-0680.2024.03","DOIUrl":"https://doi.org/10.18778/0138-0680.2024.03","url":null,"abstract":"Decidability of monadic first-order classical logic was established by Löwenheim in 1915. The proof made use of a semantic argument, but a purely syntactic proof has never been provided. In the present paper we introduce a syntactic proof of decidability of monadic first-order logic in innex normal form which exploits G3-style sequent calculi. In particular, we introduce a cut- and contraction-free calculus having a (complexity optimal) terminating proof-search procedure. We also show that this logic can be faithfully embedded in the modal logic T.","PeriodicalId":505659,"journal":{"name":"Bulletin of the Section of Logic","volume":"177 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139849938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Paracomplete Versions of Jaśkowski's Discussive Logic 论雅兹科夫斯基论辩逻辑的准完备版本
Bulletin of the Section of Logic Pub Date : 2024-01-04 DOI: 10.18778/0138-0680.2024.01
Krystyna Mruczek-Nasieniewska, Yaroslav Petrukhin, V. Shangin
{"title":"On Paracomplete Versions of Jaśkowski's Discussive Logic","authors":"Krystyna Mruczek-Nasieniewska, Yaroslav Petrukhin, V. Shangin","doi":"10.18778/0138-0680.2024.01","DOIUrl":"https://doi.org/10.18778/0138-0680.2024.01","url":null,"abstract":"Jaśkowski's discussive (discursive) logic D2 is historically one of the first paraconsistent logics, i.e., logics which 'tolerate' contradictions. Following Jaśkowski's idea to define his discussive logic by means of the modal logic S5 via special translation functions between discussive and modal languages, and supporting at the same time the tradition of paracomplete logics being the counterpart of paraconsistent ones, we present a paracomplete discussive logic D2p.","PeriodicalId":505659,"journal":{"name":"Bulletin of the Section of Logic","volume":"39 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139386672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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