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Bulletin of the Section of Logic最新文献

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A Modified Subformula Property for the Modal Logic S4.2 模态逻辑S4.2的修改子公式属性
Bulletin of the Section of Logic Pub Date : 2019-03-30 DOI: 10.18778/0138-0680.48.1.02
M. Takano
{"title":"A Modified Subformula Property for the Modal Logic S4.2","authors":"M. Takano","doi":"10.18778/0138-0680.48.1.02","DOIUrl":"https://doi.org/10.18778/0138-0680.48.1.02","url":null,"abstract":"The modal logic S4.2 is S4 with the additional axiom ◊□A ⊃ □◊A. In this article, the sequent calculus GS4.2 for this logic is presented, and by imposing an appropriate restriction on the application of the cut-rule, it is shown that, every GS4.2-provable sequent S has a GS4.2-proof such that every formula occurring in it is either a subformula of some formula in S, or the formula □¬□B or ¬□B, where □B occurs in the scope of some occurrence of □ in some formula of S. These are just the K5-subformulas of some formula in S which were introduced by us to show the modied subformula property for the modal logics K5 and K5D (Bull Sect Logic 30(2): 115–122, 2001). Some corollaries including the interpolation property for S4.2 follow from this. By slightly modifying the proof, the finite model property also follows.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44000754","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: 3
Erratum to: Congruences and Ideals in a Distributive Lattice with Respect to a Derivation 关于导子的分配格中的同余和理想的勘误表
Bulletin of the Section of Logic Pub Date : 2019-03-30 DOI: 10.18778/0138-0680.48.1.05
H. Barzegar
{"title":"Erratum to: Congruences and Ideals in a Distributive Lattice with Respect to a Derivation","authors":"H. Barzegar","doi":"10.18778/0138-0680.48.1.05","DOIUrl":"https://doi.org/10.18778/0138-0680.48.1.05","url":null,"abstract":"The present note is an Erratum for the two theorems of the paper \"Congruences and ideals in a distributive lattice with respect to a derivation\" by M. Sambasiva Rao.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43657801","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: 2
Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E 相关逻辑E的两个无穷大前极大扩张序列
Bulletin of the Section of Logic Pub Date : 2019-03-30 DOI: 10.18778/0138-0680.48.1.03
Lidia Typańska-Czajka
{"title":"Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E","authors":"Lidia Typańska-Czajka","doi":"10.18778/0138-0680.48.1.03","DOIUrl":"https://doi.org/10.18778/0138-0680.48.1.03","url":null,"abstract":"The only maximal extension of the logic of relevant entailment E is the classical logic CL. A logic L ⊆ [E,CL] called pre-maximal if and only if L is a coatom in the interval [E,CL]. We present two denumerable infinite sequences of premaximal extensions of the logic E. Note that for the relevant logic R there exist exactly three pre-maximal logics, i.e. coatoms in the interval [R,CL].","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45664469","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: 2
Positive Implicative Soju Ideals in BCK-Algebras bck -代数中的正蕴涵Soju理想
Bulletin of the Section of Logic Pub Date : 2019-03-30 DOI: 10.18778/0138-0680.48.1.01
X. Xin, R. Borzooei, Y. Jun
{"title":"Positive Implicative Soju Ideals in BCK-Algebras","authors":"X. Xin, R. Borzooei, Y. Jun","doi":"10.18778/0138-0680.48.1.01","DOIUrl":"https://doi.org/10.18778/0138-0680.48.1.01","url":null,"abstract":"The notion of positive implicative soju ideal in BCK-algebra is introduced, and several properties are investigated. Relations between soju ideal and positive implicative soju ideal are considered, and characterizations of positive implicative soju ideal are established. Finally, extension property for positive implicative soju ideal is constructed.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47984467","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: 2
Functional Completeness in CPL via Correspondence Analysis 基于对应分析的CPL中的功能完备性
Bulletin of the Section of Logic Pub Date : 2019-03-30 DOI: 10.18778/0138-0680.48.1.04
Dorota Leszczynska-Jasion, Y. Petrukhin, V. Shangin, M. Jukiewicz
{"title":"Functional Completeness in CPL via Correspondence Analysis","authors":"Dorota Leszczynska-Jasion, Y. Petrukhin, V. Shangin, M. Jukiewicz","doi":"10.18778/0138-0680.48.1.04","DOIUrl":"https://doi.org/10.18778/0138-0680.48.1.04","url":null,"abstract":"Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only branching rule is the rule of cut. The calculi pertain to classical propositional logic and any of its fragments that may be obtained from adding a set (sets) of rules characterizing a two-argument Boolean function(s) to the negation fragment of classical propositional logic. The properties of soundness and completeness of the calculi are demonstrated. The proof of completeness is conducted by Kalmár's method. \u0000Most of the presented sequent-calculus rules have been obtained automatically, by a rule-generating algorithm implemented in Python. Correctness of the algorithm is demonstrated. This automated approach allowed us to analyse thousands of possible rules' schemes, hundreds of rules corresponding to Boolean functions, and to nd dozens of those invertible. Interestingly, the analysis revealed that the presented proof-theoretic framework provides a syntactic characteristics of such an important semantic property as functional completeness.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44149929","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: 5
Labeled Sequent Calculus for Orthologic 正形学的标记序列演算
Bulletin of the Section of Logic Pub Date : 2018-12-30 DOI: 10.18778/0138-0680.47.4.01
Tomoaki Kawano
{"title":"Labeled Sequent Calculus for Orthologic","authors":"Tomoaki Kawano","doi":"10.18778/0138-0680.47.4.01","DOIUrl":"https://doi.org/10.18778/0138-0680.47.4.01","url":null,"abstract":"Orthologic (OL) is non-classical logic and has been studied as a part of quantumlogic. OL is based on an ortholattice and is also called minimal quantum logic. Sequent calculus is used as a tool for proof in logic and has been examinedfor several decades. Although there are many studies on sequent calculus forOL, these sequent calculi have some problems. In particular, they do not includeimplication connective and they are mostly incompatible with the cut-eliminationtheorem. In this paper, we introduce new labeled sequent calculus called LGOI, and show that this sequent calculus solve the above problems. It is alreadyknown that OL is decidable. We prove that decidability is preserved when theimplication connective is added to OL.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47939342","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: 3
On Injective MV-Modules 关于内射mv模块
Bulletin of the Section of Logic Pub Date : 2018-12-30 DOI: 10.18778/0138-0680.47.4.04
R. Borzooei, S. S. Goraghani
{"title":"On Injective MV-Modules","authors":"R. Borzooei, S. S. Goraghani","doi":"10.18778/0138-0680.47.4.04","DOIUrl":"https://doi.org/10.18778/0138-0680.47.4.04","url":null,"abstract":"In this paper, by considering the notion of MV-module, which is the structure that naturally correspond to lu-modules over lu-rings, we study injective MV-modules and we investigate some conditions for constructing injective MV-modules. Then we define the notions of essential A-homomorphisms and essential extension of A-homomorphisms, where A is a product MV-algebra, and we get some of there properties. Finally, we prove that a maximal essential extension of any A-ideal of an injective MV-module is an injective A-module, too.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41479021","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: 1
On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories 论Leśniewski的Copula“is”在某些类本体论理论中的可定义性
Bulletin of the Section of Logic Pub Date : 2018-12-30 DOI: 10.18778/0138-0680.47.4.02
Marcin Łyczak, A. Pietruszczak
{"title":"On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories","authors":"Marcin Łyczak, A. Pietruszczak","doi":"10.18778/0138-0680.47.4.02","DOIUrl":"https://doi.org/10.18778/0138-0680.47.4.02","url":null,"abstract":"We formulate a certain subtheory of Ishimoto’s [1] quantifier-free fragment of Leśniewski’s ontology, and show that Ishimoto’s theory can be reconstructed in it. Using an epimorphism theorem we prove that our theory is complete with respect to a suitable set-theoretic interpretation. Furthermore, we introduce the name constant 1 (which corresponds to the universal name ‘object’) and we prove its adequacy with respect to the set-theoretic interpretation (again using an epimorphism theorem). Ishimoto’s theory enriched by the constant 1 is also reconstructed in our formalism with into which 1 has been introduced. Finally we examine for both our theories their quantifier extensions and their connections with Leśniewski’s classical quantified ontology.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43657620","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: 1
Rule-Generation Theorem and its Applications 规则生成定理及其应用
Bulletin of the Section of Logic Pub Date : 2018-12-30 DOI: 10.18778/0138-0680.47.4.03
Andrzej Indrzejczak
{"title":"Rule-Generation Theorem and its Applications","authors":"Andrzej Indrzejczak","doi":"10.18778/0138-0680.47.4.03","DOIUrl":"https://doi.org/10.18778/0138-0680.47.4.03","url":null,"abstract":"In several applications of sequent calculi going beyond pure logic, an introduction of suitably defined rules seems to be more profitable than addition of extra axiomatic sequents. A program of formalization of mathematical theories via rules of special sort was developed successfully by Negri and von Plato. In this paper a general theorem on possible ways of transforming axiomatic sequents into rules in sequent calculi is proved. We discuss its possible applications and provide some case studies for illustration.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49315998","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: 7
A comparison of two systems of point-free topology 两个无点拓扑系统的比较
Bulletin of the Section of Logic Pub Date : 2018-10-30 DOI: 10.18778/0138-0680.47.3.04
Rafał Gruszczyński, A. Pietruszczak
{"title":"A comparison of two systems of point-free topology","authors":"Rafał Gruszczyński, A. Pietruszczak","doi":"10.18778/0138-0680.47.3.04","DOIUrl":"https://doi.org/10.18778/0138-0680.47.3.04","url":null,"abstract":"This is a spin-off paper to [3, 4] in which we carried out an extensive analysis of Andrzej Grzegorczyk’s point-free topology from [5]. In [1] Loredana Biacino and Giangiacomo Gerla presented an axiomatization which was inspired by the Grzegorczyk’s system, and which is its variation. Our aim is to compare the two approaches and show that they are slightly different. Except for pointing to dissimilarities, we also demonstrate that the theories coincide (in the sense that their axioms are satisfied in the same class of structures) in presence of axiom stipulating non-existence of atoms.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41966650","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: 1
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