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Bulletin of the Section of Logic最新文献

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On interpolation in NEXT(KB.Alt(2)) NEXT中的插值(KB.Alt(2))
Bulletin of the Section of Logic Pub Date : 2018-10-30 DOI: 10.18778/0138-0680.47.3.02
Zofia Kostrzycka
{"title":"On interpolation in NEXT(KB.Alt(2))","authors":"Zofia Kostrzycka","doi":"10.18778/0138-0680.47.3.02","DOIUrl":"https://doi.org/10.18778/0138-0680.47.3.02","url":null,"abstract":"We prove that there is infinitely many tabular modal logics extending KB.Alt(2) which have interpolation.","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":"45211319","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 Post-style proof of completeness theorem for symmetric relatedness Logic S 对称关联逻辑完备性定理的Post-style证明
Bulletin of the Section of Logic Pub Date : 2018-10-30 DOI: 10.18778/0138-0680.47.3.05
Mateusz Klonowski
{"title":"A Post-style proof of completeness theorem for symmetric relatedness Logic S","authors":"Mateusz Klonowski","doi":"10.18778/0138-0680.47.3.05","DOIUrl":"https://doi.org/10.18778/0138-0680.47.3.05","url":null,"abstract":"One of the logic defined by Richard Epstein in a context of an analysis of subject matter relationship is Symmetric Relatedness Logic S. In the monograph [2] we can find some open problems concerning relatedness logic, a Post-style completeness theorem for logic S is one of them. Our paper introduces a solution of this metalogical issue.","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":"43572201","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: 8
Identity, equality, nameability and completeness. Part II 同一性、平等性、可命名性和完整性。第二部分
Bulletin of the Section of Logic Pub Date : 2018-10-30 DOI: 10.18778/0138-0680.47.3.01
M. Manzano, M. C. Moreno
{"title":"Identity, equality, nameability and completeness. Part II","authors":"M. Manzano, M. C. Moreno","doi":"10.18778/0138-0680.47.3.01","DOIUrl":"https://doi.org/10.18778/0138-0680.47.3.01","url":null,"abstract":"This article is a continuation of our promenade along the winding roads of identity, equality, nameability and completeness. We continue looking for a place where all these concepts converge. We assume that identity is a binary relation between objects while equality is a symbolic relation between terms. Identity plays a central role in logic and we have looked at it from two different points of view. In one case, identity is a notion which has to be defined and, in the other case, identity is a notion used to define other logical concepts. In our previous paper, [16], we investigated whether identity can be introduced by definition arriving to the conclusion that only in full higher-order logic with standard semantics a reliable definition of identity is possible. In the present study we have moved to modal logic and realized that here we can distinguish in the formal language between two different equality symbols, the first one shall be interpreted as extensional genuine identity and only applies for objects, the second one applies for non rigid terms and has the characteristic of synonymy. We have also analyzed the hybrid modal logic where we can introduce rigid terms by definition and can express that two worlds are identical by using the nominals and the @ operator. We finish our paper in the kingdom of identity where the only primitives are lambda and equality. Here we show how other logical concepts can be defined in terms of the identity relation. We have found at the end of our walk a possible point of convergence in the logic Equational Hybrid Propositional Type Theory (EHPTT), [14] and [15].","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":"44457544","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
B-almost distributive fuzzy lattice B-几乎分配模糊格
Bulletin of the Section of Logic Pub Date : 2018-10-30 DOI: 10.18778/0138-0680.47.3.03
Berhanu Assaye, Mihret Alemneh, Gerima Tefera
{"title":"B-almost distributive fuzzy lattice","authors":"Berhanu Assaye, Mihret Alemneh, Gerima Tefera","doi":"10.18778/0138-0680.47.3.03","DOIUrl":"https://doi.org/10.18778/0138-0680.47.3.03","url":null,"abstract":"The paper introduces the concept of B-Almost distributive fuzzy lattice (BADFL) in terms of its principal ideal fuzzy lattice. Necessary and sufficient conditions for an ADFL to become a B-ADFL are investigated. We also prove the equivalency of B-algebra and B-fuzzy algebra. In addition, we extend PSADL to PSADFL and prove that B-ADFL implies PSADFL.","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":"43701912","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: 4
Variable Sharing in Substructural Logics: an Algebraic Characterization 子结构逻辑中的变量共享：代数表征
Bulletin of the Section of Logic Pub Date : 2018-06-30 DOI: 10.18778/0138-0680.47.2.03
Guillermo Badia
{"title":"Variable Sharing in Substructural Logics: an Algebraic Characterization","authors":"Guillermo Badia","doi":"10.18778/0138-0680.47.2.03","DOIUrl":"https://doi.org/10.18778/0138-0680.47.2.03","url":null,"abstract":"We characterize the non-trivial substructural logics having the variable sharing property as well as its strong version. To this end, we find the algebraic counterparts over varieties of these logical properties.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46704356","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
Grzegorczyk Algebras Revisited Grzegorczyk代数重述
Bulletin of the Section of Logic Pub Date : 2018-06-30 DOI: 10.18778/0138-0680.47.2.05
Michał M. Stronkowski
{"title":"Grzegorczyk Algebras Revisited","authors":"Michał M. Stronkowski","doi":"10.18778/0138-0680.47.2.05","DOIUrl":"https://doi.org/10.18778/0138-0680.47.2.05","url":null,"abstract":"We provide simple algebraic proofs of two important facts, due to Zakharyaschev and Esakia, about Grzegorczyk algebras.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47739376","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
Pseudo-BCH Semilattices Pseudo-BCH Semilattices
Bulletin of the Section of Logic Pub Date : 2018-06-30 DOI: 10.18778/0138-0680.47.2.04
A. Walendziak
{"title":"Pseudo-BCH Semilattices","authors":"A. Walendziak","doi":"10.18778/0138-0680.47.2.04","DOIUrl":"https://doi.org/10.18778/0138-0680.47.2.04","url":null,"abstract":"In this paper we study pseudo-BCH algebras which are semilattices or lattices with respect to the natural relations ≤; we call them pseudo-BCH join-semilattices, pseudo-BCH meet-semilattices and pseudo-BCH lattices, respectively. We prove that the class of all pseudo-BCH join-semilattices is a variety and show that it is weakly regular, arithmetical at 1, and congruence distributive. In addition, we obtain the systems of identities defininig pseudo-BCH meet-semilattices and pseudo-BCH lattices.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43114477","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
Free Modal Pseudocomplemented De Morgan Algebras 自由模态伪补De Morgan代数
Bulletin of the Section of Logic Pub Date : 2018-06-30 DOI: 10.18778/0138-0680.47.2.02
A. Figallo, Nora Oliva, A. Ziliani
{"title":"Free Modal Pseudocomplemented De Morgan Algebras","authors":"A. Figallo, Nora Oliva, A. Ziliani","doi":"10.18778/0138-0680.47.2.02","DOIUrl":"https://doi.org/10.18778/0138-0680.47.2.02","url":null,"abstract":"Modal pseudocomplemented De Morgan algebras (or mpM-algebras) were investigated in A. V. Figallo, N. Oliva, A. Ziliani, Modal pseudocomplemented De Morgan algebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 53, 1 (2014), pp. 65–79, and they constitute a proper subvariety of the variety of pseudocomplemented De Morgan algebras satisfying xΛ(∼x)* = (∼(xΛ(∼x)*))* studied by H. Sankappanavar in 1987. In this paper the study of these algebras is continued. More precisely, new characterizations of mpM-congruences are shown. In particular, one of them is determined by taking into account an implication operation which is defined on these algebras as weak implication. In addition, the finite mpM-algebras were considered and a factorization theorem of them is given. Finally, the structure of the free finitely generated mpM-algebras is obtained and a formula to compute its cardinal number in terms of the number of the free generators is established. For characterization of the finitely-generated free De Morgan algebras, free Boole-De Morgan algebras and free De Morgan quasilattices see: [16, 17, 18].","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46590357","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
Categorical Abstract Algebraic Logic: Pseudo-Referential Matrix System Semantics 范畴抽象代数逻辑：伪参考矩阵系统语义
Bulletin of the Section of Logic Pub Date : 2018-06-30 DOI: 10.18778/0138-0680.47.2.01
G. Voutsadakis
{"title":"Categorical Abstract Algebraic Logic: Pseudo-Referential Matrix System Semantics","authors":"G. Voutsadakis","doi":"10.18778/0138-0680.47.2.01","DOIUrl":"https://doi.org/10.18778/0138-0680.47.2.01","url":null,"abstract":"This work adapts techniques and results first developed by Malinowski and by Marek in the context of referential semantics of sentential logics to the context of logics formalized as π-institutions. More precisely, the notion of a pseudoreferential matrix system is introduced and it is shown how this construct generalizes that of a referential matrix system. It is then shown that every π–institution has a pseudo-referential matrix system semantics. This contrasts with referential matrix system semantics which is only available for self-extensional π-institutions by a previous result of the author obtained as an extension of a classical result of Wójcicki. Finally, it is shown that it is possible to replace an arbitrary pseudoreferential matrix system semantics by a discrete pseudo-referential matrix system semantics.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45088745","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 Note on some Characterization of Distributive Lattices of Finite Length 有限长度分配格的若干性质的注记
Bulletin of the Section of Logic Pub Date : 2015-01-01 DOI: 10.18778/0138-0680.44.1.2.02
Marcin Łazarz, Krzysztof Siemienczuk
{"title":"A Note on some Characterization of Distributive Lattices of Finite Length","authors":"Marcin Łazarz, Krzysztof Siemienczuk","doi":"10.18778/0138-0680.44.1.2.02","DOIUrl":"https://doi.org/10.18778/0138-0680.44.1.2.02","url":null,"abstract":"Using known facts we give a simple characterization of the distributivity of lattices of finite length.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67609789","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
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