Bulletin of the Section of Logic
https://www.czasopisma.uni.lodz.pl/bulletin
<div style="text-align: justify;"> <p>The <em>Bulletin of the Section of Logic</em> (<em>BSL</em>) is a quarterly peer-reviewed journal published with the support of the Lodz University Press. The <em>BSL</em> was founded in 1972 by Ryszard Wójcicki, Head of the Section of Logic of the Polish Academy of Sciences, then based in Wrocław, as a newsletter-journal designed for the exchange of scientific results among members of the Section with their national and international partners and colleagues. The first editor-in-chief of the <em>BSL</em> was Jan Zygmunt, who supervised the editorial process of the first six issues of the journal. In 1973 the role was taken over by Marek Tokarz. From 1975 to 2018 the journal was managed and edited by Grzegorz Malinowski. In 1992 the Department of Logic at the University of Łódź took over the publication from the Polish Academy of Sciences changing its policy into regular peer-reviewed journal. The aim of the <em>Bulletin</em> is to act as a forum for the prompt wide dissemination of original, significant results in logic through rapid publication. The <em>BSL</em> welcomes especially contributions dealing directly with logical calculi, their methodology, application and algebraic interpretations.</p> </div>Wydawnictwo Uniwersytetu Łódzkiegoen-USBulletin of the Section of Logic0138-0680Linear Abelian Modal Logic
https://www.czasopisma.uni.lodz.pl/bulletin/article/view/13976
<p>A many-valued modal logic, called linear abelian modal logic \(\rm {\mathbf{LK(A)}}\) is introduced as an extension of the abelian modal logic \(\rm \mathbf{K(A)}\). Abelian modal logic \(\rm \mathbf{K(A)}\) is the minimal modal extension of the logic of lattice-ordered abelian groups. The logic \(\rm \mathbf{LK(A)}\) is axiomatized by extending \(\rm \mathbf{K(A)}\) with the modal axiom schemas \(\Box(\varphi\vee\psi)\rightarrow(\Box\varphi\vee\Box\psi)\) and \((\Box\varphi\wedge\Box\psi)\rightarrow\Box(\varphi\wedge\psi)\). Completeness theorem with respect to algebraic semantics and a hypersequent calculus admitting cut-elimination are established. Finally, the correspondence between hypersequent calculi and axiomatization is investigated.</p>Hamzeh Mohammadi
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2023-12-152023-12-1553112810.18778/0138-0680.2023.30On Paracomplete Versions of Jaśkowski's Discussive Logic
https://www.czasopisma.uni.lodz.pl/bulletin/article/view/14000
<p>Jaśkowski's discussive (discursive) logic <strong>D2</strong> 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 <strong>S5</strong> <em>via</em> 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 <strong>D2<sup>p</sup></strong>.</p>Krystyna Mruczek-NasieniewskaYaroslav PetrukhinVasily Shangin
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2024-01-042024-01-04531296110.18778/0138-0680.2024.01Mathematical Methods in Region-Based Theories of Space: The Case of Whitehead Points
https://www.czasopisma.uni.lodz.pl/bulletin/article/view/14245
<p>Regions-based theories of space aim—among others—to define <em>points </em>in a geometrically appealing way. The most famous definition of this kind is probably due to Whitehead. However, to conclude that the objects defined are points indeed, one should show that they are points of a geometrical or a topological space constructed in a specific way. This paper intends to show how the development of mathematical tools allows showing that Whitehead’s method of extensive abstraction provides a construction of objects that are fundamental building blocks of specific topological spaces.</p>Rafał Gruszczyński
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2023-12-042023-12-045316310410.18778/0138-0680.2023.29Stabilizers on \(L\)-algebras
https://www.czasopisma.uni.lodz.pl/bulletin/article/view/16040
<p>The main goal of this paper is to introduce the notion of stabilizers in \(L\)-algebras and develop stabilizer theory in \(L\)-algebras. In this paper, we introduced the notions of left and right stabilizers and investigated some related properties of them. Then, we discussed the relations among stabilizers, ideal and co-annihilators. Also, we obtained that the set of all ideals of a \(CKL\)-algebra forms a relative pseudo-complemented lattice. In addition, we proved that right stabilizers in \(CKL\)-algebra are ideals. Then by using the right stabilizers we produced a basis for a topology on \(L\)-algebra. We showed that the generated topology by this basis is Baire, connected, locally connected and separable and we investigated the other properties of this topology.</p>Gholam Reza RezaeiMona Aaly Kologani
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2023-11-202023-11-2053110512410.18778/0138-0680.2023.28\(L\)-Modules
https://www.czasopisma.uni.lodz.pl/bulletin/article/view/16380
<p>In this paper, considering \(L\)-algebras, which include a significant number of other algebraic structures, we present a definition of modules on \(L\)-algebras (\(L\)-<em>modules</em>). Then we provide some examples and obtain some results on \(L\)-modules. Also, we present definitions of <em>prime ideals</em> of \(L\)-algebras and \(L\)-<em>submodules</em> (<em>prime</em> \(L\)-<em>submodules</em>) of \(L\)-modules, and investigate the relationship between them. Finally, by proving a number of theorems, we provide some conditions for having prime \(L\)-submodules.</p>Simin Saidi GoraghaniRajab Ali Borzooei
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2023-12-042023-12-0453112514410.18778/0138-0680.2023.27