Bulletin of the Section of Logic https://czasopisma.uni.lodz.pl/bulletin <div style="text-align: justify;"> <p>The&nbsp;<em>Bulletin of the Section of Logic</em>&nbsp;(<em>BSL</em>) is a quarterly peer-reviewed journal published with the support of the Lodz University Press. The&nbsp;<em>BSL</em>&nbsp;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. From1975 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&nbsp;<em>Bulletin</em>&nbsp;is to act as a forum for the prompt wide dissemination of original, significant results in logic through rapid publication. The&nbsp;<em>BSL</em>&nbsp;welcomes especially contributions dealing directly with logical calculi, their methodology, application and algebraic interpretations.</p> </div> Wydawnictwo Uniwersytetu Łódzkiego en-US Bulletin of the Section of Logic 0138-0680 Super-Strict Implications https://czasopisma.uni.lodz.pl/bulletin/article/view/7996 <p>This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the S5-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic.</p> Guido Gherardi Eugenio Orlandelli Copyright (c) 2021 https://creativecommons.org/licenses/by-nc-nd/4.0 2021-01-20 2021-01-20 50 1 1 34 10.18778/0138-0680.2021.02 A Semi-lattice of Four-valued Literal-paraconsistent-paracomplete Logics https://czasopisma.uni.lodz.pl/bulletin/article/view/7710 <p>In this paper, we consider the class of four-valued literal-paraconsistent-paracomplete logics constructed by combination of isomorphs of classical logic<em> CPC</em>. These logics form a 10-element upper semi-lattice with respect to the functional embeddinig one logic into another. The mechanism of variation of paraconsistency and paracompleteness properties in logics is demonstrated on the example of two four-element lattices included in the upper semi-lattice. Functional properties and sets of tautologies of corresponding literal-paraconsistent-paracomplete matrices are investigated. Among the considered matrices there are the matrix of Puga and da Costa's logic V and the matrix of paranormal logic <em>P</em><em><sup>1</sup></em><em>I<sup>1</sup></em>, which is the part of a sequence of paranormal matrices proposed by V. Fernández.</p> Natalya Tomova Copyright (c) 2020 https://creativecommons.org/licenses/by-nc-nd/4.0 2020-11-13 2020-11-13 50 1 35 53 10.18778/0138-0680.2020.24 One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity https://czasopisma.uni.lodz.pl/bulletin/article/view/8117 <p>Bilinear Logic of Lambek amounts to Noncommutative MALL of Abrusci. Lambek proves the cut–elimination theorem for a one-sided (in fact, left-sided) sequent system for this logic. Here we prove an analogous result for the nonassociative version of this logic. Like Lambek, we consider a left-sided system, but the result also holds for its right-sided version, by a natural symmetry. The treatment of nonassociative sequent systems involves some subtleties, not appearing in associative logics. We also prove the PTime complexity of the multiplicative fragment of NBL.</p> Paweł Płaczek Copyright (c) 2021 https://creativecommons.org/licenses/by-nc-nd/4.0 2020-11-13 2020-11-13 50 1 55 80 10.18778/0138-0680.2020.25 On GE-algebras https://czasopisma.uni.lodz.pl/bulletin/article/view/8189 <p>Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive GE-algebras.</p> Ravikumar Bandaru Arsham Borumand Saeid Young Bae Jun Copyright (c) 2021 https://creativecommons.org/licenses/by-nc-nd/4.0 2020-08-30 2020-08-30 50 1 81 96 10.18778/0138-0680.2020.20 Soju Filters in Hoop Algebras https://czasopisma.uni.lodz.pl/bulletin/article/view/8610 <p>The notions of (implicative) soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju sub-hoop, a soju filter and an implicative soju filter are discussed. Conditions for a soju filter to be implicative are displayed, and characterizations of an implicative soju filters are considered. The extension property of an implicative soju filter is established.</p> Rajab Ali Borzooei Gholam Reza Rezaei Mona Aaly Kologhani Young Bae Jun Copyright (c) 2021 https://creativecommons.org/licenses/by-nc-nd/4.0 2020-12-30 2020-12-30 50 1 97 123 10.18778/0138-0680.2020.28