Bulletin of the Section of Logic 50/1 (2021)
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Soju Filters in Hoop Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)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 ... -
On GE-algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-08-30)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 ... -
One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-11-13)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 ... -
A Semi-lattice of Four-valued Literal-paraconsistent-paracomplete Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-11-13)In this paper, we consider the class of four-valued literal-paraconsistent-paracomplete logics constructed by combination of isomorphs of classical logic CPC. These logics form a 10-element upper semi-lattice with respect ... -
Super-Strict Implications
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-01-20)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 ...